# math

tan theta= 15/8 and pi< theta<3pi/2

a. Sin(- theta)
b. cos2theta
c. sin( theta - 3pi/4)
d. cos(theta/2)

can someone explain to me how do you find the exact value for these?

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1. the angle is in the 3rd quadrant.
So, draw a diagram where the hypotenuse extends down to the left from (0,0)

Since tan = y/x, this means that y = -15 and x = -8. So the hypotenuse of your triangle goes from (0,0) to (-8,-15), length=17

Now you are ready to go.

sin theta = y/h = -15/17
cos theta = x/h = -8/17

Use these values in your double-angle, half-angle, and sum/difference formulas.

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