Inverse Trigonometric FunctionsVideos, worksheets, games and acivities to help PreCalculus students learn how about the inverse trigonometric functions.
An Introduction to Inverse Trigonometric Functions
Inverse Sine Function : Since sine is not a one-to-one function, the domain must be limited to -pi/2 to pi/2, which is called the restricted sinefunction. The inverse sine function is written as sin^-1(x) or arcsin(x). Inverse functions swap x- and y-values, so the range of inverse sine is -pi/2 to ?/2 and the domain is -1 to 1. When evaluating problems, use identities or start from the inside function.
Inverse Cosine Function : Since cosine is not a one-to-one function, the domain must be limited to 0 to pi, which is called the restrictedcosine function. The inverse cosine function is written as cos^-1(x) or arccos(x). Inverse functions swap x- and y-values, so the range of inverse cosine is 0 to pi and the domain is -1 to 1. When evaluating problems, use identities or start from the inside function.
Inverse Tangent Function : Since tangent is not a one-to-one function, the domain must be limited to -pi/2 to pi/2, which is called the restricted tangent function. The graph of the inverse tangent function is a reflection of the restricted tangent function over y = x. Note that the vertical asymptotes become horizontal, at y = pi/2 and y = -pi/2, and the domain and ranges swap for the inverse function.
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