Inverse trig function?

Question

Find the exact value of sin^-1 = (- sqrt 3/2)

Answer 1

Just plot the point. Sine is opp/ hypot. So -sqrt 3 is the opposite and 2 is the hyp. since the first number is negative, it points down. Since the second number is negative, it is in the positive quadrant. So the angle lies in the 4th quadrant, where only cosine is positive. In the first quadrant, sin^-1 (sqrt3/2) = pi/3, which is 60 degrees. In quadrant 4, it is 300 degrees, or 5pi/3.

Answer 2

the easiest way to do this is on a graphing calculator, graph:

y = sin^-1
y = sqrt(1.5)

look for the intersection of the graphs, the x-value at the intersection is your answer.

Answer 3

sin θ = - √3 / 2
θ = 240° , 300°