# Thread: Trigonomteric Ratios and Special Angles

1. ## Trigonomteric Ratios and Special Angles

Can someone please explain to me how to solve this question:

Determine an exact value for each expression:

a) [cot(pi/4)]/[(cos(pi/3))(csc(pi/2))]

b) [cos(pi/6)][csc(pi/3)]+sin(pi/4)

even if you explain one of them, that would be appreciated! I don't understand this question at all, so please be detailed.

thank you so much

2. Originally Posted by skeske1234
Can someone please explain to me how to solve this question:

Determine an exact value for each expression:

a) [cot(pi/4)]/[(cos(pi/3))(csc(pi/2))]

b) [cos(pi/6)][csc(pi/3)]+sin(pi/4)

even if you explain one of them, that would be appreciated! I don't understand this question at all, so please be detailed.

thank you so much
you're expected to know these values from your knowledge of basic identities and values of trig ratios on the unit circle ...

$\cot\left(\frac{\pi}{4}\right) = \frac{\cos\left(\frac{\pi}{4}\right)}{\sin\left(\f rac{\pi}{4}\right)} = 1$

$\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}$

$\csc\left(\frac{\pi}{2}\right) = \frac{1}{\sin\left(\frac{\pi}{2}\right)} = 1$

$\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$

$\csc\left(\frac{\pi}{3}\right) = \frac{1}{\sin\left(\frac{\pi}{3}\right)} = \frac{2}{\sqrt{3}}$

$\sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$

use these values to evaluate each expression.