Evaluate. sin^-1(cos(π)/(6))

Name: Problem 49, Chapter 7: Algebra and Trigonometry
Uploaded: 2020-07-08T01:41:29-08:00
Duration: 1 min 5 s
Channel: Ankit Gupta
Description: Evaluate. sin^-1(cos(π)/(6))

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Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions, such as the arcsine function, return the angle whose trigonometric value equals a given number. Understanding these functions involves knowing that the range of the arcsine function is restricted (typically to [-?/2, ?/2]) to ensure that it is a proper inverse function.

Domain and Range of Inverse Trigonometric Functions

The domain of the arcsine function is limited to [-1, 1], and its range is confined to the interval [-?/2, ?/2]. These restrictions are crucial for correctly interpreting the output of inverse trigonometric functions and for ensuring the uniqueness of the inverse function.

Co-function Identities

Co-function identities relate sine and cosine functions through complementary angles. For example, the identity cos(?) = sin(?/2 - ?) can simplify the evaluation of expressions involving inverse sine of a cosine value by converting the cosine term into a corresponding sine expression.

Standard Trigonometric Values

Mastery of standard trigonometric values is fundamental in trigonometry. Knowing the sine, cosine, and other trigonometric function values for common angles (like ?/6, ?/4, and ?/3) is essential for simplifying and evaluating trigonometric expressions accurately.

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