Understanding and Evaluating the Inverse Sine Function: sin^-1(√3/2)

Sin^-1 (√3/2)

To find the value of sin^-1(√3/2), we need to find the angle whose sine is equal to √3/2

To find the value of sin^-1(√3/2), we need to find the angle whose sine is equal to √3/2.

The sine function (sin) is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. The range of the sine function is between -1 and 1.

For the given value √3/2, we can visualize it by drawing a right triangle with the opposite side of length √3 and the hypotenuse of length 2. This is an example of a special triangle called a 30-60-90 triangle, where the angles are 30 degrees, 60 degrees, and 90 degrees.

Using the Pythagorean theorem, we can find the length of the adjacent side of the triangle:

(Adjacent)^2 + (Opposite)^2 = (Hypotenuse)^2
(Adjacent)^2 + (√3)^2 = (2)^2
(Adjacent)^2 + 3 = 4
(Adjacent)^2 = 1
Adjacent = 1

So, the length of the adjacent side is 1.

Now, we can find the angle whose sine is √3/2. Looking at our triangle, we can see that the angle opposite the side of length √3 is 60 degrees (or π/3 radians).

Therefore, sin^-1 (√3/2) = 60 degrees (or π/3 radians).

Note: The sin^-1 function, also known as the arcsine function, is the inverse of the sine function, and it returns the angle whose sine is equal to the given value.

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