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Explain why sin^ -1 (sin ( 3 pi 4 )+ 3 pi 4 when y = sin x and y = sin^1(x) are inverses

User Hanna
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Answer:

The inverse function of a trigonometric function, such as the sine, is called arcsine or sin^-1. To show that the inverse function of sine, sin^-1(x), and the value of x when y = sin(x) are inverses, we can use the definition of the inverse function.

When y = sin(x), this means that x = sin^-1(y). Substituting sin(3π/4) in place of y gives x = sin^-1(sin(3π/4)).

Using the trigonometric identity of the inverse function, we have that:

cos^-1(cos(x)) = x

This means that sin^-1(sin(3π/4)) = 3π/4. Therefore, x = sin^-1(sin(3π/4)) + 3π/4, which means that the value of x is equal to the sum of sin^-1(sin(3π/4)) and 3π/4.

In summary, it can be shown that sin^-1(sin(3π/4)) + 3π/4 = 3π/4, which shows that the inverse function of sine and the value of x when y = sin(x) are reverse. This is because the inverse sine function takes the y value and returns the corresponding x value, and the sine function takes the x value and returns the corresponding y value.

Explanation:

User Steffen Frank
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