Inverse Sine, Cosine and TangentA series of free High School Trigonometry Video Lessons from Brightstorm.
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 sine function. 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 restricted cosine 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.
Using the Inverse Trigonometric Functions In a problem where two trig functions are not inverses of each other (also known as "inverse trigonometric functions", (1) replace the inverse function with a variable (which represents an angle), (2) use the definition of the inverse function to draw the angle in the unit circle and identify one coordinate, (3) find the missing coordinate (use Pythagorean Theorem, for example), (4) use the coordinates to find the missing value.
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