Inverse Trigonometric Functions Worksheet

The inverse trigonometric functions worksheet is an invaluable tool for anyone seeking to deepen their understanding of these mathematical concepts. Designed for students and learners of all levels, this worksheet provides a comprehensive and structured approach to exploring the properties and applications of inverse trigonometric functions. Whether you are a high school student preparing for exams, a college student studying advanced math, or a curious individual seeking to expand your knowledge, this worksheet is the perfect resource to help you grasp the complexities of inverse trigonometric functions.

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What is the inverse function of sin(x)?

The inverse function of sin(x) is arcsin(x), also denoted as sin^(-1)(x), which represents the inverse sine function. This function finds the angle whose sine is a given number x, in the domain of -1 to 1, and returns an angle within the range of -?/2 to ?/2.

What is the inverse function of cos(x)?

The inverse function of cos(x) is arccos(x) or cos^(-1)(x), which is also known as the inverse cosine function. This function gives the angle whose cosine is x, providing the original input to the cosine function can be retrieved by evaluating the inverse cosine function on the output.

What is the inverse function of tan(x)?

The inverse function of tan(x) is arctan(x), also denoted as tan^(-1)(x), or atan(x).

What is the value of arcsin(0.5)?

The value of arcsin(0.5) is approximately 30 degrees or ?/6 radians.

What is the value of arccos(0.8)?

The value of arccos(0.8) is approximately 36.87 degrees or 0.6435 radians.

What is the value of arctan(1)?

The value of arctan(1) is ?/4 radians or 45 degrees.

What is the domain of the inverse sine function?

The domain of the inverse sine function, also known as arcsine function, is [-1, 1]. This means that the input values for arcsine should lie within the closed interval from -1 to 1 in order to produce a valid output, which typically lies in the interval [-?/2, ?/2].

What is the range of the inverse cosine function?

The range of the inverse cosine function, denoted as arccos or cos^-1, is from 0 to ?, or in radians [-?/2, ?/2], which corresponds to angles between 0 and 180 degrees. This function maps input values between -1 and 1 to output values between 0 and ?.

What is the range of the inverse tangent function?

The range of the inverse tangent function is from negative pi/2 to positive pi/2, or -?/2 < tan^(-1)(x) < ?/2, where x is any real number.

What is the principal value of arcsin(1.2)?

The principal value of arcsin(1.2) does not exist because the sine function has a maximum value of 1, and 1.2 is outside of this range.