Precalculus : Graphs and Inverses of Trigonometric Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #1 :Graphing Inverse Trig Functions

State the domain and range ofand.

Possible Answers:

domain:

range:

domain:

range:

domain:, such that

range:

domain:

range:

domain:

range:

domain:

range:

domain:

range:

domain:

range:

domain:

range:

domain:

range:, such that

Correct answer:

domain:, such that

range:

domain:

range:

Explanation:

The two graphs help provide a visual. The domain is all possible x values, and the range is all possible y values. The arctan function exchanges all x and y values of the tangent function. However, in order to continue being a function (by passing the horizontal line test), the arctangent function's range is restricted to. It is not a coincidence that the range of the tangent function is equal to the domain of the arctangent function because of the nature of inverse relationships.

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domain:, such that

range:

domain:

range:

You can see that while therange and thedomain match, thedomain and therange are not exact matches; this is so thatcan be a function (by being restricted).

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