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# Pythagorean Identities

Trigonometric identities bring new life to the Pythagorean theorem by re-envisioning the legs of a right triangle as sine and cosine.

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 \(\sin^2 \theta + \cos^2 \theta \)?

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