Without using a calculator, find the exact values of

1. $$\sin \left(\frac{\pi }{12}\right)\text{ and }\cos \left(\frac{\pi }{12}\right)$$
2. $$\sin \left(\frac{7\pi }{12}\right)\text{ and }\cos \left(\frac{7\pi }{12}\right)$$

For (a),

For (b), either use

or you can use

and make use of part (a)