I really need help with trig!?

Question

How do I do the following? I just need to get started and I am very confused about these. If someone can help me on any one of these, it would be greatly appreciated.

Find tan -150 degrees without a calculator
Find csc of 3pi over 2 w/o calculator
Find sec 5pi/4 w/o calculator
Sin of theta = 4.5678 (true or false) Why?
Sin of 100 degrees is (<,+,>) sin of 110 degrees. Why?

Answer 1

For tan of 150 degrees, you should draw a graph of 150 degrees on a coordinate plane. (it's so hard to explain trig. with words) So the result should be 30 degrees on the second quadrant. And since tangent is opposite over adjacent and using 30, 60, 90-degree special triangle, tangent of 150 degrees would be -1/sqr(3) or -sqr(3)/3

Answer 2

Are you familiar with the Unit Circle and SOHCAHTOA?

If not, make yourself familiar with them since these 2 basic concepts will be something you use all throughout Calculus as well

-150 Degress can also be written as -5pi/6 or 7pi/6. Sin of 7pi/6 is -1/2. Cos of 7pi/6 is -3(2^[1/2])/2. Tan is Sin/Cos so Tan(7pi/6) = 2^(1/2)/6

Using your identities and the unit circle will help you find the remaining answers with the exception of the forth question. There may be a piece of that missing that would allow us to answer it.

Answer 3

number 2: The cscof 3pi over two is at the 270degrees line (straight down). We know this because pi over two is ninety degrees. I don't know how to explain that to you, but it's just one of those things you learn to memorize from using it so much (and should memorize cause it's just that important). so ninety degrees is equal to pi over two. 180 degrees is equal to 2pi over 2 or pi. the 270 degrees is equal to threepi over two whose coordinates are (0, -1) sin is the opposite of csc. Sin is y over r (and r=radius, which since this is the unit circle is one). So you can say csc = r over y , so 1 over -1= -1 which is your answer.

I know this seems like a lot of work, but really isn't. Just a lot of explaining. :D good luck with other problems, email me if you need more help.

Answer 4

look in the index of your math book for the "unit circle"...it is the only way to solve those problems w/o a calculator. If you cant find it in your book its on this site...

http://www.iccc.cc.ia.us/mathscience/Haugen/Unit%20Circle.JPG

the way you use it is that you go to the location (for example 3pi/2 in the second problem) and you'll see a coordinate pair at that location. The first number in parentheses is the cos, the second is the sin, and tan is the numerator of sin over the numerator of cos. I realize that is kind of confusing but it will most likely explain it a lot bettter in your text book. Good Luck!

Answer 5

http://www.nmhschool.org/math/mat521/unit_circle.bmp maybe this picture will help you. for example if you have to find the sin of 5pi over 6, you look for 5pi over six on the unit cirlce and you know that sin is the y in cordinates so your answer would be one half. while the cos of 5pi over six is the square root of 3 over two. you just have to know some things like csc= 1/sin, sec=1/cos, and so on. i hope i was of some help.