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Working with unit circle in trigonometry through vertical line

Some extra questions from NCERT Exemplar problem, CBSE Support material and other books explaining working with coterminal and allied angles

Working with the unit circle in trigonometry (on horizontal and vertical line)

Example 9 Find the value of cos (–1710°).

 NCERT Exercise 3.3

Prove that:

1. $$\sin^2 \frac{\pi}{6} + \cos^2 \frac{\pi}{3} – \tan^2 \frac{\pi}{4} = – \frac{1}{2}$$

3. $$\cot^2 \frac{\pi}{6}+\cosec \frac{5\pi}{6} + 3 \tan^2 \frac{\pi}{6}=6$$