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Sine, cosine, and tangent have two quadrants that are more important than the others. It is important to isolate those quadrants for the inverse functions. Sine and cosine functions have a range restriction, which means their inverses have to have a domain restriction. The domain restriction of the inverse results in a range restriction. The values on the Unit Circle are not unique; it is necessary to restrict the inverse functions so the values do not repeat. The sine, cosine, and tangent functions are cyclical and repeat output values. When the graph is reflected over y=x the resulting graph is not a function.

Sine, cosine, and tangent have two quadrants that are more important than the others. It is important to isolate those quadrants for the inverse functions. Sine and cosine functions have a range restriction, which means their inverses have to have a domain restriction. The domain restriction of the inverse results in a range restriction. The values on the Unit Circle are not unique; it is necessary to restrict the inverse functions so the values do not repeat. The sine, cosine, and tangent functions are cyclical and repeat output values. When the graph is reflected over y=x the resulting graph is not a function.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 81E
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Which is NOT a good reason why having domain and range restrictions for the inverse trig functions is important?

Sine, cosine, and tangent have two quadrants that are more important than the others. It is important to isolate those quadrants for the inverse functions. Sine and cosine functions have a range restriction, which means their inverses have to have a domain restriction. The domain restriction of the inverse results in a range restriction. The values on the Unit Circle are not unique; it is necessary to restrict the inverse functions so the values do not repeat. The sine, cosine, and tangent functions are cyclical and repeat output values. When the graph is reflected over y=x the resulting graph is not a function.
Transcribed Image Text:Sine, cosine, and tangent have two quadrants that are more important than the others. It is important to isolate those quadrants for the inverse functions. Sine and cosine functions have a range restriction, which means their inverses have to have a domain restriction. The domain restriction of the inverse results in a range restriction. The values on the Unit Circle are not unique; it is necessary to restrict the inverse functions so the values do not repeat. The sine, cosine, and tangent functions are cyclical and repeat output values. When the graph is reflected over y=x the resulting graph is not a function.
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