SOLUTION: i was wondering how you do these problems: The directions are to find the exact value of each expression. 6 cos 3π/4+ 2tan(-π/3) and sec ( -π/3)- cot (-5π/

Algebra ->  Trigonometry-basics -> SOLUTION: i was wondering how you do these problems: The directions are to find the exact value of each expression. 6 cos 3π/4+ 2tan(-π/3) and sec ( -π/3)- cot (-5π/      Log On


   

Question 203109: i was wondering how you do these problems: The directions are to find the exact value of each expression.
6 cos 3π/4+ 2tan(-π/3)
and
sec ( -π/3)- cot (-5π/4)
please i am struggling to do this work. I would appreciate if you would explain in detail. Thank you in advance.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, first off let's bring up the unit circle




This is a very handy tool. For each given angle (located on the spokes of the wheel), there is a point that lies on the circle. It turns out that the x coordinate of the point refers to the cosine of that given angle. Likewise, the y coordinate of the point refers to the sine of that angle.

For example, the cosine of pi%2F3 is cos%28pi%2F3%29=1%2F2 since the x coordinate of this point is x=1%2F2. Also, the sine of pi%2F3 is sin%28pi%2F3%29=sqrt%282%29%2F2 since the y coordinate of this point is y=sqrt%282%29%2F2. You can use the unit circle to evaluate the sine/cosine of any given angle shown.


Finally, remember that we have the following identities:

tan%28x%29=sin%28x%29%2Fcos%28x%29

sec%28x%29=1%2Fcos%28x%29

cot%28x%29=1%2Ftan%28x%29=cos%28x%29%2Fsin%28x%29



I hope this will refresh something or help you get started. If this didn't help, please let me know or repost.