Geometry
Pythagorean Identities
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 \( \sin \theta\cos \theta \)?