Evaluate sin^-1(-1/2)?

Question

Is it either:
-pi/3
pi/3
pi/6
-pi/6

Answer 1

It is the angle whose sin = -1/2.

That's a 30-degree angle in the 4th quadrant, so it's -pi/6.

Answer 2

The expression "sin^-1 (-1/2)" means "Give me an angle in either the first or fourth quadrant whose sine is -1/2." The sin-1 function ALWAYS gives an angle between -pi/2 and pi/2, inclusive. There will always be one unique angle in this interval that works.

In this case, the appropriate angle is -pi/6, because sin (-pi/6) = -1/2, and -pi/2 <= -pi/6 <= pi/2.

Answer 3

The three preceding answers have given you only one solution, namely - pi/6.

However, there are TWO solutions, one in the third, and one in the fourth quadrant.

Recall that sin (pi/6) = 1/2.

But sin (-x) = - sin (x); so sin (-pi/6) = -1/2. (Everyone's answer, so far.)

Also, sin (pi - y) = sin (y) --- no matter what the sign of y. So, if y = -pi/6, sin (pi + pi/6) = sin (-pi/6) = -1/2.

So, the two solutions are: - pi/6 (4th quadrant) and 7pi/6 or -5pi/6 (3rd quadrant).

Live long and prosper.

Answer 4

-30 degrees. Which would be -pi/6 radians.

Answer 5

x = sin^-1 ( -1/2)
use sin on both sides
sin(x) = sin ( sin^-1 (-1/2) )
sin(x) = -1/2
x = -pi/6

Answer 6

- pi/6

Answer 7

-pi/6