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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.

#### Challenge Quizzes

What is the value of $\sin ^2 10 ^ \circ + \sin ^2 20 ^ \circ + \sin ^2 30 ^ \circ + \sin ^2 40 ^ \circ \\ + \sin ^2 50 ^ \circ + \sin ^2 60 ^ \circ + \sin ^2 70 ^ \circ + \sin ^2 80 ^ \circ ?$

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

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

If $$\sin \theta+ \cos \theta = \frac {1}{2}$$, what is the value of $$\tan \theta+\cot \theta$$?

If $$\tan \theta+ \cot \theta = 3$$, what is the value of $$\sin \theta\cos \theta$$?

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