Question

How do you find the sin of 7pi/6 with no calculator? I know you need to use to unit circle but I'm stuck after that.

Answer 1

OK this is one way to do it: 7pi/6 can be written as pi+pi/6. Now sin(pi+pi/6) is what (take a guess)? And what would be its sign (take a guess again, you can find it using the unit circle)??

Answer 2

OK. I hope you know this: sin(pi+anything) = sin(anything). Ofcourse, the sign may be different, and by anything we mean less than pi. Now 7pi/6 is in the third quadrant, and sine is negative in the third quadrant. Hence, the answer to your question is -0.5