Find the Value Using the Unit Circle arcsin(-1)

Problem

arcsin(−1)

Solution

1. Identify the definition of the inverse sine function, y=arcsin(x) which requires finding an angle θ such that sin(θ)=x within the restricted range [−π/2,π/2]

2. Locate the value −1 on the yaxis of the unit circle, as the sine of an angle corresponds to the ycoordinate of a point on the unit circle.

3. Determine the angle in the interval [−π/2,π/2] where the ycoordinate is −1

4. Observe that at the bottom of the unit circle, the coordinate is (0,−1) which corresponds to the angle −π/2 radians or −90

Final Answer

arcsin(−1)=−π/2

Want more problems? Check here!