# How do you apply the fundamental identities to values of theta and show that they are true?

Jan 9, 2015

you may try using angles that are "easy" to deal with, i.e., you know the values of the trigonometric functions associated with them,such as, $\pi , \frac{\pi}{2} , \frac{\pi}{3} , \frac{\pi}{4} , \frac{\pi}{3}$.

Consider: ${\sin}^{2} \left(\theta\right) + {\cos}^{2} \left(\theta\right) = 1$
Chose $\theta = \frac{\pi}{3}$ (or 60○ if you like).
You have:
$\sin \left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$
$\cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$

Substituting in ${\sin}^{2} \left(\theta\right) + {\cos}^{2} \left(\theta\right)$ you get:
$\frac{3}{4} + \frac{1}{4} = 1$

You may now use the same approach to all the other identities to check if they work.
I hope it helped.