# Thread: Function value + - or undefined

1. ## Function value + - or undefined

Determine whether the function value is positive, negative, zero or undefined.

tan 25 degree = my answer = positive?
cot Pi = how do you get this?
cos -2pi/5 = negative?
sin -pi/2 = negative?
csc 0 = how do you get this?

Also I have a issue with another part of the worksheet, it says determine the quadrant the pheta terminates...

how do i get this?

a couple of the problems are
2.) cos pheta <0, sin pheta <0

how do you solve those?

2. tan (25 degrees) is positive and sin (-pi/2) is negative.

For cos (-2pi/5), remember cos (-2pi/5) = cos (2pi/5).

To calculate cot pi, cot x = 1/(tan x).

To calculate csc 0, csc x = 1/(sin x).

3. huh? why is the cos positive?
and i still dont understand the cot or csc

4. Wait so cot would be pi/(tan pi) = 0
and csc would be 0/(sin 0) = 0
???

5. The cos is positive because $\displaystyle \frac{-2\pi}{5}$ is in the fourth quadrant, where x is positive, and hence the cos is positive. Or you can use the identity I used, which is cos(-x) = cos x.

For the other two problems, I used identities again. Can you calculate $\displaystyle \frac{1}{\tan \pi}$ and $\displaystyle \frac{1}{\sin 0}$?

Edit: the identities are $\displaystyle \cot x = \frac{1}{\tan x}$ and $\displaystyle \csc x = \frac{1}{\sin x}$.

6. so cot pi = 1/ tan pi = 1 / 0 = 0
and csc 0 = 1/ sin 0 = 1 / 0 = 0?

would it always be a 1 at the top is that like the equation for cot and csc?

7. Originally Posted by cokeclassic
would it always be a 1 at the top is that like the equation for cot and csc?
For those two identities, yes.

Also, 1/0 is undefined.

8. Ok, so how would you know which number goes on the top?

9. Originally Posted by cokeclassic
Ok, so how would you know which number goes on the top?
Just remember

$\displaystyle \sec x = \frac{1}{\cos x}$

$\displaystyle \csc x = \frac{1}{\sin x}$

$\displaystyle \cot x = \frac{1}{\tan x}$

for all x.

10. thanks!