Geometry
# Pythagorean Identities

What is the value of

$\sin^2 30 ^ \circ + \cos^2 30 ^\circ?$

What is the value of

$\sin^2 \dfrac{\pi}{3} + \cos^2 \dfrac{\pi}{3}?$

If $\sin \theta = \frac { 1}{3}$, what is the value of $\cos^2 \theta$?

If $\cos \theta = \frac {\sqrt{3}}{2}$, what is the value of $1-\sin^2 \theta$?

If $\tan \theta = \frac{3}{4}$, what is the value of $\sin^2 \theta + \cos^2 \theta$?