Question

Sin(θ) = −

9

41

where

3π

2

< θ < 2π

Answer 1

sin theta = -9/41, where theta is in Q IV; find the angle theta:

Here the opp side is -9, the hyp. is 41. The adj side is found by applying the Pyth. Thm.:

(-9)^2 + x^2 = 41^2

81 + x^2 = 1681. Then x^2 = 1600, and the adj. side (x) is +40. We know it's +40 because theta is in Q IV.

The angle theta is arcsin (-9/41). Using a calculator,

arcsin (-9/41) = -0.22 radians (which is correct because theta is in Q IV, just as -0.22 rad is in Q IV. You could express theta as a positive angle by subtracting 0.22 rad from 2pi rad: 1.78 rad. You could, of course, change these angles in radians into angles in degrees.