﻿ Inverse Sin 1 and -1 : Special cases of the Inverse of Sine Function

# Inverse Sin 1 and sin-1(-1)

Examples, Pictures and Significance

The inverse sin of 1, ie sin-1 (1) is a very special value for the inverse sine function. Remember that sin-1(x) will give you the angle whose sine is x . Therefore, sin-1 (1) = the angle whose sine is 1.

### The Value of the Inverse Sin of 1

As you can see below, the inverse sin-1 (1) is 90° or, in radian measure, Π/2 . '1' represents the maximum value of the sine function .It happens at Π/2 and then again at 3Π/2 etc.. (see second graph below) Below is a picture of the graph sin(x) with over the domain of 0 ≤x ≤4Π with sin(1) indicted by the black dot. As you can see the graph of the sine function has a value of 1 at Π /2 and again at 5Π/2 and 9Π/2 and every 2Π thereafter.

### The Value of the Inverse Sin of -1

As you can see below, the sin-1 (1) is 270° or, in radian measure, 3Π/2 . '1' represents the minimum value of the sine function ever gets and happens at Π/2 and then again at 3Π/2 etc.. (See graph at bottom) Below is a picture of the graph of sin(x) with over the domain of 0 ≤x ≤4Π with sin(-1) indicted by the black dot. As you can see from the graph, sine has a value of -1 at 3Π /2 and again at 7Π/2 and 11Π/2 and every 2Π thereafter.

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