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..

Inverse sine 1 rule
(see second graph below)
Picture of Inverse sine of 1

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.

Inverse sine of 1 long graph

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..

Inverse sine 1 rule
(See graph at bottom)
Picture of Inverse Sine of negative 1

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.

graph of sin ivnerse of negative 1