Reflection 11

This week was a struggling week for me, because the stuff that we learn earlier in the week and last week ididnt know how to do. Now i feel strongly about what im doing now. This week was all about Trig. ; the unit circle and the trig chart played major roles in learning every thing we did.

Unit Circle
90 degrees =(0,1) ; pi/2
180 degrees= (-1,0) ; pi
270 degrees = (0,-1); 3pi/2
360 degrees = (1,0); 2pi

sin= y/r
cos=x/r
tan=y/x
csc=r/y
sec=r/x
cot=x/y

Turing degree into Radian is D*pi/180
Turning radian into Degree is R*180/pi

Reflection #11

Okay this week wasn't that bad with spirit week going on and all. It really psyched me up, and this week's math wasn't that hard. We learned more about trig this week, and on Friday, we learned about right triangles. I will explain these.

You can use the acronym SOHCAHTOA, to determine this:

sin (theta) = opposite leg / hypotenuse

cos (theta) = adjacent leg / hypotenuse

tan (theta) = opposite leg / adjacent leg

As well as in plain trigonometry, csc, sec, and cot are found by "flipping" the original values.

Example:

For triangle ABC, a=40, angleA=28 degrees, and angleC is 90 degrees. Solve for b and c.

First you would draw the triangle.

Then take the tangent of 28 degrees, because it deals with the opposite and adjacent sides.

tan 28 degrees = 40/b

b tan 28 degrees = 40

b = 40/tan 28 degrees = 75.229

Then take the sine of 28 degrees, because it deals with the opposite and hypotenuse.

sin 28 degrees = 40/c

c = 40/sin 28 degrees = 85.202

The only thing I don't really understand is the word problem where it says to find the measures of the acute angles of a 3-4-5 right triangle...Help please? Thanks.

Reflection

So where to begin? This week was great as always because of spirit week! But well lets get to the math part of this blog. Trig! that one word should explain it all. Its not that hard but then in some ways its not as easy. We took our chapter 7 test on thursday, i thought it was tough, but other people might have different opinions. I found the easiest thing with chapter 7 was the conversion from degrees to radians and radians to degrees. Also, converting degrees to degrees, minutes, seconds was simple. OH and that trig chart, well yeah good thing i can memorize easily because its alot, but overall pretty simple to comprehend. I'll give the unit circle then a few conversions for examples.

EXAMPLES:

90 degrees, (0,1), pi/2
360 degrees, (1,0), 2pi
180 degrees, (-1,0), pi
270 degrees, (0,-1), 3pi/2

sin = y/r
cos = x/r
tan = y/x
csc = r/y
sec = r/x
cot = x/y

1.) sin 2pi = y/r = 0/1 = 0
2.) cos 180 degrees = x/r = -1/1 = -1
3.) sec 3pi/2 = r/x = 1/0 = undefined

Though that is easy, i sill have trouble with inverses and word problems. Those are definitely my weak spot.

Reflection #10!

Wow, ten reflections already!
well, as for trig i'm actually catching on, which comes as a huge surprise to myself.
I pretty much understand everything except the word problems that involve diameter and apparent size?

A few things that i remember for this week are:

sin=y/r
cos=x/r
tan=y/x
cot=x/y
csc=r/y
sec=r/x

ALSO:
degrees to radians= D * pi/180
radians to degrees= R * 180/pi(in this case, pi's cancel leaving you with a number in DEGREES)

ALSO:
coterminal angles either add or subtract 360 to an angle.

---------------
as i said in the beginning, i do not completely understand anything dealing with solving for diameter or apparent size. any word problem with S, K, R, THETA, i can do fine. but as for diameter with scientific notation, latitude, planets, etc. i'm LOST!

help?

Reflection 10

This week we learned a lot of trig. Trig seems easy as long as you know the formulas. We are not moving as fast as we did in the first nine weeks so it is easy to learn. I am going to have to study for the chapter test on Monday. In 7-1 to convert degrees to radians you have to multipy the degrees by pi/180. To convert radians to degrees you take the radian and multiply by 180/pi.

Ex: 225 degrees x pi/180 = 5/4 pi

3pi/4 x 180/pi=135 degrees

In 7-3 you have to know the unit circle and chart.

The Chart:

Sin=y/r Csc=r/y
Cos=x/r Sec=r/x
tan=y/x Cot=x/y

Ex:

Find all 6 trig functions of (-3,4).

Sin=4/5 Csc=5/4
Cos=-3/5 Sec=-5/3
tan=-4/3 Cot=-3/4

The unit circle:

90 degrees= pi/2 and (0,1)

180 degrees=pi and (-1,0)

270 degrees=3pi/2 and (0,-1)

360 degrees= 2pi and (1,0)



Also for 7-4 and 7-5 you have to learn a chart but, I do not get 7-6. That is inverses and i am not sure what to do.

Reflection #10

in the coarse of us learning trig. this week i am completely lost. the only thing i really know how to do is:

switch to radiants:

take your number and times it by (pie/180)

and to find seconds, minutes, etc:

you take your number behind the decimal and multiply by 60.

and to find seconds you divide your answer by 3600

on the other hand, im completely lost with everything else...

maybe its because i havent taken the time to memorize the trig. chart yet, im not sure.

i get on the right track and then somewhere along the lines, I GET LOST!

REFLECTION 10 I THINK

So, I'm pretty confindent with all this trig stuff. But the quizzes seem to say otherwise. I still think I'm good at it. Your trig functions are:
sin=y/r
tan=y/x
sec=r/x
cos=x/r
cot=x/y
csc=r/y

Theta is the measure of an angle. Angles are measured in either degrees or radians. to convert from degrees to radians you multiply by Pi/180 and to convert from radians to degrees you multiply by 180/Pi.
If you have degrees in decimal form and would like to convert it to degrees minutes' seconds" you multiply the decimal by 60 and whatever is to the left of the decimal is your minutes. If there is anything to the right of the decimal then you multiply that by 60 to give you your seconds. Ex:123.45 degrees is 123 degrees 27' 0"

To find a reference angle you: find which quadrant the angle is in, determine the sign in that quadrant, then subtract 180 Degrees until you get something in between 90 and 0 degrees.Ex: sin 210 degrees. 210 degrees is in the third quadrant. sin is y/r so your angle is negative. 210-180=30 so your reference angle is -sin 30 degrees

If anyone knows how to find the reference angle of an angle with no trig sign please help. This was in the probs and stats paper for adv. math. example the reference angle of 120 degrees. would it be 60 degrees?

Relfection 10

This week we learned trigonometry. This deals with triangles. Angles are measured in degrees, minutes, seconds. To find the minutes multiply what is behind decimal by 60. To find seconds multiply what is behind decimal of minutes by 60, divide by 3600 to get decimals. Angles are measured in degree and radians. Radians equal pie over 180. Degrees equal radius times 180 over pie.. Never plug in pie to the calculater. To find the coterminal angle add or subtract 360. Must always use degree symbol when in degrees. to find a sector of a circle you do radius times theta. To find an area of a sector do kequal to 1/2 radius sector. To find the six trig function u do sin=y/r cos=x/r tan=y/x csc=r/y sec=r/x cot=x/y. Trig inverses are easy, and right now i am studying the trig chart. Tri isnt that hard you just have to study and do your homework. I just had trouble with the unit circle but i got that down pack now.

Reflection #10

For what I understand: conversions

To convert degrees to radians: multiply by pi/180
ex. 120 degrees
120 times pi/180
(keep answer in pi form)
120 divided by 180
=2/3
your answer =2/3 pi or =2 pi/3

To convert radians to degrees: multiply by 180/pi
ex. 3 pi/4
3 pi/4 times 180/pi
pi cacels out
3/4 times 180
your answer =135 degrees

To convert degrees to radians, it has to be in decimal form:
119.2
37.92
and so forth
119.2/180 (plug in cal.) =149/225
then multiply pi
your answer =149 pi/225

To convert degrees decimals to minutes and seconds:
take the decimal of the degrees and multiply by 60 for minutes
68.33 .33 times 60 =19.8
take the decimal of the minutes and multiply by 60 for seconds
19.8 .8 times 60 =48
your answer =68 degrees 19 minutes 48 seconds

*if seconds have decimal, round to the 3rd decimal
*if minutes don't have decimal, leave in degrees minutes

To convert degrees minutes seconds to decimals:
68 degrees 19 minutes 48 seconds
divide seconds (48) by 3600 =.013
divide minutes (19) by 60 =.317
add the two together =.33
your answer =68.33

Now for what I don't understand: I have no idea how to do sin 2 pi or cot 3 pi/4 or any of that kind of thing. We've had that on several quizzes and I still don't know what I'm doing. And the unit circle, I know it, but not how to apply it. And the trig chart...I'm not sure how to apply that either. But especially the word problems, I have no idea what's going on with those. Any help? Please?

reflection #10

this week we started to cover trigonometry, including conversions, functions, the trig chart, and inverses. The trig chart wasnt that confusing, just the memorization of it was what needed to happen.

(* = square root of)

0 degrees sin0=0 cos0=1 tan0=0 csc0=undefined sec0=1 cot0=undefined

30 degrees 1/2 *3/2 *3/3 2 2*3/3 *3

45 degrees *2/2 *2/2 1 *2 *2 1

60 degrees *3/2 1/2 *3 2*3/3 2 *3/3

90 degrees 1 0 undefined 1 undefined 0

sin cos tan csc sec cot

this is the trig chart, it is used mainly to find reference angles:

reference angles: must be between 0-90 degrees

1.) find which quadrant angle is in
2.) determine the sign +ve or -ve
3.) subtract 180 degrees until the angle is between |0-90 degrees|

sin 45 degrees = (square root)2/2
cos pi/3 = 1/2

sin 270 degrees = -sin 30 degrees = -1/2
cos 315 degrees = cos 45 degrees = (square root)2/2

reflection 10

I thought this week was sooo hard. I didn't understand much. I like failed every quiz we had this week:/ Hopefully I can remember the trig chart and do pretty good on our test tuesday. From 7-3, I did understand that.

Sin, circle thing,- Y/R
cos, circle thing,- X/R
tan, circle thing,- Y/X

csc, circle thing, R/Y
sec, circle thing, R/X
cot, circle thing, X/Y

its pretty easy, the bottom part is just opposite from the top..

EXAMPLE:

(1,-1) Find all six trig functions.

a^2+b^2=c^2

sin- -1/square root of 2 = -square root of 2/2

cos- 1/square root of 2 = square root of 2/2

tan- -1/1 = -1

csc- square root of 2/-1 = -square root of 2

sec- square root of 2/1 = square root of 2

cot- 1/-1 = -1

I don't really understand some stuff from 7-4, like when you start subtracting 180 and 360. I get a little lost there..and i also don't really understand the trig inverses from 7-6..

Reflection 10

Okay, another week goes by, in chapter 7. This chapter will get confusing if you dont memorize a whole lot of formulas, ESPECIALLY the trig chart and unit circle :P. I did however get this down quickly.

sin=y/r
tan=y/x
sec=r/x
cos=x/r
cot=x/y
csc=r/y

im still working on the trig chart though, but i do still remember how to convert degrees and radians

15.4d= 15d (.4 X 60)= 15d 24m

12d 14m 11s = 12d + 14/60 + 11/3600 = 12.236d

radians = d X pi/180

degrees = rads X 180/pi

^ in my opinion this is the easiest part of the chapter to remember

section 7-2

S = R0 0=theta

K = 1/2 r^2 0 or K = 1/2 rs (depending on the problem)

0 = angle
K = area of sector
r = radius

FINDING THE REFERENCE ANGLE/ANSWER

sin 270d
subtract 180
sin 90d 90 is the reference angle
1 is the value


TRIG INVERSES

moving:
I ==> IV make theta -ve
I ==> III add 180d
I ==> II -theta + 180d
II => IV add 180d

the angle must be positive in order to be a final answer

sin^-1 (-3/2)
using the trig chart, the reference angle is 60d

move to the 3rd and 4th quadrant

60 + 180 = 240
-60 + 360 = 300

This should be a general overview of what i currently know. im having some trouble with the word problems.
now to do my english essay >:}

Reflection #10

OMG...chapter 7 involves a lot of studying,well all of the other chapters did too, but this one was the most stuff we had to learn, i think. We learned sin, cos, tan, cot, sec, & csc.

6 Trig Functions:

sin= y/r
cos= x/r
tan= y/x
cot= x/y
sec= r/x
csc= r/y

Now here is an example of when you have to find them.

EX: Find all 6 Trig functions for (-3,4)

First you have to find your radius.

r= square root of (-3)^2 + (4)^2
r= square root of 9 + 6
r= square root of 25
r= 5

Now find all of the functions.

sin= 4/5
cos= -3/5
tan= 4/-3
cot= -3/4
sec= 5/-3
csc= 5/4

(BTW, I got all of the problems like this wrong on my quizzes because I forgot how to find the radius :/ )

______________________________________________________________________

The trig chart is easy if you study.

0 degrees: sin 0 = 0
30 degrees: sin pi/6 = 1/2
45 degrees: sin pi/4 = square root of 2/ 2
60 degrees: sin pi/3 = square root of 3/ 2
90 degrees: sin pi/2 = 1

Now for cos, the chart just flips, so cos pi/2 = 0 and cos 0 = 1

tan 0 = 0
tan pi/6 = square root of 3/ 2
tan pi/4 = 1
tan pi/3 = square root of 3
tan pi/2 = undefined

Now for cot, the chart just flips, so cot 0 = undefined and cot pi/2 = 0.

sec 0 = 1
sec pi/6 = 2 square root of 3/ 3
sec pi/4 = square root of 2
sec pi/3 = 2
sec pi/2 = undefined

Now for csc, the chart just flips, so csc 0 = undefined and csc pi/2 = 1.

______________________________________________________________________

When you find a coterminal angle, you just add or subtract 360 degrees until you get your answer. If you are asked to find the negative coterminal angle of 2234, you just keep subtracting 360 degrees until you get a negative number.

Now for the things that I did not understand, The word problems confused me, but they probably confuse everybody else too. I also did not get the inverse thing, but we only been working on it for a day, so it should get better. But if anyone wants to give me an inverse problem, it would be appreciated. THANKS :)

reflection 10

This week was full of the glorious subject of trigonometry. Haha I lied about the glorious part. Anyway, we learned a bunch of stuff about trig functions, and I'm gunna help you out with trig functions. Cos, Tan, Csc.............they're all the same in one way. You need to study your behind off. Study all ways to find trig functions. Period. Then study your trig chart....but that a different story. Tonight I'm going to explain how to find all of the trig functions by being told only a point on a graph.......here we go.

The first thing you need to know if your trig functions and what they are equal to:

sin*= y/r
cos*= x/r
tan*= y/x
csc*= r/y
sec*= r/x
cot*= x/y
*denotes theta

ok now you are given a point...let's say, (3,4)
Now you would usually draw a graph but i can't do that on a computer so here's the shortcut:
Let 3=a and 4=b. On the graph you make a right triangle. So now that you have a and b what are you going to do? That's right, use your formula for to find the hypotenuse of a right triangle: a^2 + b^2 = c^2

So your hypotenuse = 5

now, x=3 y=4 and r=5 because your hypotenuse is r.

Now you plug that into the handy dandy trig functions you memorized. So:

sin=4/5
cos=3/4
tan=4/3
csc=5/4
sec=4/3
cot=3/4

Yay you did it! Congratulations!

___________________________________________________________
I basically understood everything, the only reason i'm still shaky on some stuff is because i'm still memorizing stuff. Although the word problems, like example 3 on page 277 is really tough and I could probably use some help in that.

reflection 10

Hey peoples!!! So lsu, the saints, and us won this week, never thought that would ever happen lol! So we learned about trigonometry this week and it confuses the hell out of me! The only thing that i actually understood was the six trig functions and the trig chart, but i still dont remember the whole chart! Its really big and confusing, but once you realize the pattern, its still kinda hard, lol, but more simple than it looks!

but here are the six trig functions!
sin theta= y/r
cos theta =x/r
tan theta=y/x
sec theta=r/x
csc theta=r/y

cot theta=x/y

Simple right?!

oh yeah and i understood the unit circle:

90 degrees=pi/2, (0,1)

360 degrees=2pi, (1,0)

270 degrees=3pi/2, (0,-1)

180 degrees=pi, (-1,0)

and that is what i understood, what confuses me is the word problems! anyone wanna help with that????

oh yeah, and if anyone has an extremely easy way to remember the chart...that would be extremely helpful! because i have one but its kinda confusing and i dont know if im gonna rember it and it only works for like half of it and the test is on TUESDAY!!!!! at least we gonna be in some kinda comfortable clothing from the spirit week stuff, which im doing like i do every year and wear pajamas everyday, or at least im gonna try! yerd meh?!

Reflection #10

Alright this week we learned how to find trig inverses, use the trig chart, use the unit circle, and how to find all six trig functions when given a point. The one thing that I understood the most this week is how to find all six trig functions when given a point.
Example: (1,-1) find all six trig functions.
Step 1: know that: Sin theata =y/r r = square root of x^2 + y^2
Cos theata =x/r
Tan theata =y/x
Csc theata =r/y
Sec theata =r/x
Cot theata =x/y
Step 2: draw a graph and plot the point, and draw a line from the origin to the point, then finish off the triangle and label the sides x, y, and r.
Step 3: then take the numbers from the graph and plug them into the equations from above.
Sin= -1/square root 2
Cos= 1/square root 2
Tan= -1/1
Cse= square root 2/-1
Sec= square root 2/1
Cot= 1/-1
Finished!!

***Now for something I didn’t quite understand was how to find the trig inverses. I don’t understand when you have to add 180 and when to subtract or add 360.

Reflection 10

Hey there, whoever is reading this, i see you. You don't think that i can c u, but i can. LOOK OUT! I prolly just saved ur life, makin u look around, a sniper bullet may have just passed u, and if it did, well then, ur safe :P jk jk jk jk jk, it was a joke. hahaha its so boring right now, needed a joke to wake me up :P so……………………how bout dem saints, what happened to them in the 1st half, but now they're alive and scorin and stuff. whats up with that? and theres NOTHING to do at all on a sunday, stuck at home, the saints aint doin too good eh :/ but at least its a close game. blah, that football game yesterday at Pan-American was booooooooooring, nothing exciting happened. to the ppl who took the ACT saturday, good luck on ur scores. Tuesday’s goneeeeee, with the wind, BLAH, nothin to type, im so bored :P soz..........................who’s ready for spirit week? that was sarcasm :X, DUDE, video games are the solution to boredom ;D

anyways, b4 i go play some games so im not bored out of my mind, lemme do the math part,

one thing i did understand last week was the whole trig functions stuff. it’s really easy, all u gotta do is remember the stuff for it, like where everything goes.
like: sin theta= y/r
cos theta =x/r
tan theta=y/x
cot theta=x/y
sec theta=r/x
csc theta=r/y

but i dont understand that stupid unit circle thing, i dont get it :(

and p.s. REGGIE BUSH ACTUALLY DID SOMETHING GOOD FOR ONCE, WOW :P

for 7-6 inverses.

After you find the quadrant the number goes in, how do you know what the next two quadrants are?

REFLECTION #10

So, to start off, I thought this week was actually really good. I completely understand everything we learned last week, which is good. And the things we went over this week weren't so bad either. Well on Monday the first thing we learned was sin, cos, tan, csc, sec, and cot. We used those to find all the six trig functions of a point. We also learned the unit circle which I think is extremely easy since I already memorized it. Then on Tuesday we learned the trig chart. yowww! Yeah it's definitely a lot to memorize but I'd say it's better than studying history notes. hah. We also learned how to find reference angles and exact answers. And for that you have to make sure you know your quadrants and if you're looking for exact answers you have to make sure you know the trig chart. Then on Wednesday we learned how to find trig inverses. Now this is something I'm still really iffy about because I don't know how to figure out what quadrants you need to find. I mean I payed attention in class, and I somewhat understand it but I'm still really lost. And then on Thursday we didn't have school so that was great getting an extra day off from math for once. And by the way, I'm already getting tired of having two back to back math classes everyday. Some days I feel like if I keep my eyes closed too long when I blink, I might fall asleep and never wake up. Well anyway, enought about that and back to math. On Friday we continued with what we were going over on Wednesday. We did some more practice with it but I'm still a little bit confused.

On the bright side, I did learn something this week that was super easy for me and is easy to explain. I thought finding all six trig functions was easy to follow so here's an example:

Ex. 1.) (4,3) Find all 6 trig functions.

*Okay so the first thing you have to do is draw a graph and plot the point (4,3) on it. (obviously I can't do that on here but if you write it down on paper it's easy to follow.) So after you plot the point, you make a triangle out of it by drawing a line from the origin to your dot and then draw another line from the dot straight down to the x axis. And there's your triangle! (:
Alright so you only have two sides of your triangle so you have to find your hypotenuse by plugging 3 and 4 into the Pythagorean Theorem>> a^2 + b^2 = c^2 which gives you:
3^2 + 4^2 = c^2 >> 9 + 16 = c^2 >>> 25 = c^2 (square root both sides) c=5 (*or you could have just known that a 3,4,5 triangle is a perfect triangle and you wouldn't have had to do all that nonsense :P
Alright now the next thing you need to know are your formulas:
sin theta=y/r
cos theta=x/r
tan theta=y/x
csc theta= r/y
sec theta=r/x
cot theta=x/y
(*where "r" is the length of the hypotenuse (5) )

So from there you just plug numbers into the 6 formulas and then you're done!!
final answers are:

sin theta = 3/5
cos theta = 4/5
tan theta = 3/4
csc theta = 5/3
sec theta = 5/4
cot theta = 4/3

Another thing I thought was really easy is the unit circle. It's a simple thing to memorize and it deffinitely comes in handy.

**Now for what I don't understand. which is quite a bit. Okay first I don't understand how to do those weird word problems like the ones on our quizzes. And yes! I will ask about them in class tomorrow so that I know what I'm doing for the test on Tuesday. Also, I'm having some troubles with trig inverses finding the quadrants and whatnot. If you know what I'm talking about. So if anyone would mind explaining these things (Ms.Robinson) that would be greatly appreciated :)

Reflection

Hmmm, where to begin?! This week i hated because i was sick and missed an important lesson in class. But, on monday i was there, so i did learn some easy stuff this week. Trig really isn't that bad, it's just a lot of memorizing. On monday we learned 7.3, it was about trig functions and unit circles. It basically made a lot of since to me.

TRIG:

sin theta = y/r
cos theta = x/r
tan theta = y/x
csc theta = r/y
sec theta = r/x
cot theta = x/y

Unit Circle:

90 degrees, pi/2, (0,1)
360 degrees, 2pi, (1,0)
270 degrees, 3pi/2, (0,-1)
180 degrees, pi, (-1,0)

EXAMPLES:

If 0 is the denominator, it is always undefined.
The radius always = 1.

1.) sin 90 degrees = y/r = 1/1 = 1

2.) sin 2pi = y/r = 0/1 = 0

3.) tan 3pi/2 = y/x = -1/0 = undefined

So thats just some stuff from earlier in the week, but i have the notes from tuesday and wednesday and i have no idea what they mean. Can someone PLEASE help me and explain that stuff. Thanks :)
have a great sunday. GO SAINTS!

Reflection 10

This week wasn't too bad for me, I just need to memorize everything.. including the trig chart. One thing I understand is knowing whether something is positive or negative. To find if something is positive or negative you have to find what quadrant it is in then apply the forumla to the quadrant. If your x or y is in a negative quadrant your answer will be negative.

Example:

Is sin 95 +ve or -ve? +ve
-95 is in quadrant I.
-Sin formula is y/r.
-The y in this quadrant is postive, which would make the number positive.

Example:

Is cos 212 +ve or -ve? -ve
-212 is in quadrant III.
-Cos formula is x/r
-The x in this quadrant is negative, which would make the number negative.

---------------------------------------

Something I really don't understand is the word problems we learned about the equator and stuff. Those are extremely confusing. If someone could explain them to me in a simple way that would be great.

Reflection 10

This week was very confusing to me and some stuff im still confused about but one thing i know that came easy to me was finding the refrence angles and quadrants.

*Refrence angles must be b/w 0-90 degrees or 0-pi/2

1. Find which quadrant angle its in.
2.Determine the sign in that quadrant (positive/negative)
3. subtract 180 degrees until the angle is b/w 0-90 degrees

example:

1. SIN 210

First you find out which quadrant it would be in then you make a chart and mark it....III quadrant. ( the 3rd quadr. is negative so you final answer would be neg.)

subtract 180 from 210 and you get 30.
so your answer would be -SIN 30.

2. COS 315

Find the quarant and the quadr. would be IV ( 4th qaudr. is positive so your final is pos.)

subtract 180 from 315 and you are left with 135 ( not b/w 0-90 yet)
subtract 180 from 135 again and you are left with -45
take the absolute value of that and you get 45 and thats your final answer in degree...cos 45 or square root of 2/2