And Applying The Inverse Sine Function To Find Angles

Sin^-1 (√3/2)

π/3

Let’s start by understanding what the inverse sine function means. The inverse sine function, denoted as sin^{-1}(x), is the function that gives us the angle whose sine is x. In other words, if sin(y) = x, then sin^{-1}(x) = y. This function is defined only for values of x that fall in the range [-1, 1].

Now, let’s apply this definition to the given expression:

sin^{-1}(\sqrt3/2)

We want to find the angle whose sine is \sqrt3/2. We know that the sine of 60 degrees is \sqrt3/2 (you can use the unit circle or the values of the trigonometric functions for special angles to verify this). Therefore, we can write:

sin^{-1}(\sqrt3/2) = 60 degrees

Note that there’s another angle whose sine is \sqrt3/2, namely 120 degrees. However, the inverse sine function is defined to return only one value, and for values of x between -1 and 1, it always returns a value between -90 degrees and 90 degrees (inclusive). Therefore, in this case, we take the angle between -90 degrees and 90 degrees that has a sine of \sqrt3/2, which is 60 degrees.

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