# Thread: Trig functions

1. ## Trig functions

List the 6 trig functions of 90 degrees. Which does not represent a real number?

I know what the 6 trig functions are...I just need help starting this problem. How would you set it up? Would you use the 30-60-90 triangle or the 45-45-90 triangle?

Thanks for any help!

2. Originally Posted by live_laugh_luv27
List the 6 trig functions of 90 degrees. Which does not represent a real number?

I know what the 6 trig functions are...I just need help starting this problem. How would you set it up? Would you use the 30-60-90 triangle or the 45-45-90 triangle?

Thanks for any help!
There are 6 trig functions, but all of them are based around only 2... $\displaystyle \sin(x)$ and $\displaystyle \cos(x)$. You should be able to verify that $\displaystyle \sin(90) = 1$ and $\displaystyle \cos(90) = 0$

And then remember that:

$\displaystyle \tan(x) = \frac{\sin(x)}{\cos(x)}$

$\displaystyle \text{cot}(x) = \frac{1}{\tan{x}} = \frac{\cos(x)}{\sin(x)}$

$\displaystyle \text{sec}(x) = \frac{1}{\cos(x)}$

$\displaystyle \text{cosec}(x) = \frac{1}{\sin(x)}$

Hence:

$\displaystyle \sin(90) = 1$

$\displaystyle \cos(90) = 0$

$\displaystyle \tan(90) = \frac{\sin(90)}{\cos(90)} = \frac{1}{0}$

$\displaystyle \text{cot}(90) = \frac{\cos(90)}{\sin(90)} = \frac{0}{1}$

$\displaystyle \text{sec}(90) = \frac{1}{\cos(90)} = \frac{1}{0}$

$\displaystyle \text{cosec}(90) = \frac{1}{\sin(x)} = \frac{1}{1}$

Can you evaluate which is real and which is undefined now?