Question

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

Answer 1

I am not sure about this one but here I go;
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, pi/2, pi/3, pi/4, pi/3`.

Consider: `sin^2(theta) + cos^2(theta)=1`
Chose `theta=pi/3` (or 60○ if you like).
You have:
`sin(pi/3)=sqrt(3)/2`
`cos(pi/3)=1/2`

Substituting in `sin^2(theta)+cos^2(theta)` you get:
`3/4+1/4=1`

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