1. Keeper 11 Inverses of the Trigonometric Functions
Find values of the inverse trigonometric functions.
Simplify expressions such as sin (sin -1 x) and sin -1 (sin x).
Simplify expressions involving composition such as sin (cos –1 1/2) without using a calculator.
Simplify expressions such as sin arctan (a/b) by making a drawing and reading off appropriate ratios.
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2. Copyright © 2009 Pearson Education, Inc.
Inverse Sine Function
The graphs of an equation and its inverse are reflections of each other across the line y = x.
However, the inverse is not a function as it is drawn.
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3. Copyright © 2009 Pearson Education, Inc.
Inverse Sine Function
We must restrict the domain of the inverse sine function.
It is fairly standard to restrict it as shown here.
The domain is [–1, 1].
The range is [–π/2, π/2].
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4. Inverse Cosine Function
The graphs of an equation and its inverse are reflections of each other across the line y = x.
However, the inverse is not a function as it is drawn.
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5. Inverse Cosine Function
We must restrict the domain of the inverse cosine function.
It is fairly standard to restrict it as shown here.
The domain is [–1, 1].
The range is [0, π].
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6. Inverse Tangent Function
The graphs of an equation and its inverse are reflections of each other across the line y = x.
However, the inverse is not a function as it is drawn.
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7. Copyright © 2009 Pearson Education, Inc.
Inverse Sine Function
We must restrict the domain of the inverse tangent function.
It is fairly standard to restrict it as shown here.
The domain is (–∞, ∞).
The range is (–π/2, π/2).
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8. Inverse Trigonometric Functions
Function Domain Range
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9. Graphs of the Inverse Trigonometric Functions
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10. Graphs of the Inverse Trigonometric Functions
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