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Section 4.7 handout ann_1

# Section 4.7 handout ann_1 - Section 4.7 Inverse...

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Section 4.7 Inverse Trigonometric Functions, Page 1 Section 4.7 Inverse Trigonometric Functions, Page 1

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Section 4.7 Inverse Trigonometric Functions, Page 2 Section 4.7 Inverse Trigonometric Functions, Page 2
1 -1 1 -1 1 -1 Section 4.7 Inverse Trigonometric Functions, Page 3 Section 4.7: InverseTrigonometric Functions 1) Objective 1: The Inverse Sine Function . a. Restrict domain of sine function to [- π /2, π /2] so that the inversesine function exists. Range is still [-1, 1] π /2 - π /2 π /2 - π /2 y = sin x y = sin x y = sin -1 x Domain: (- , ) ∞ ∞ Domain: [ - π /2, π /2 ] Domain: [ -1, 1 ] Range: [ -1, 1 ] Range: [ -1, 1 ] Range: [ - π /2, π /2 ] b. Denoted by: y = sin -1 x or y = arc sin x . c. It means: Find the angle whosesine is x . d. Domain: [-1, 1] Range: [- π /2, π /2] e. Graph y = sin -1 x using radian mode & window settings: x min = - 1.2 y min = - π / 2 – .1 x max = 1.2 y max = π / 2 + .1 x scale = .25 y scale = π / 8 f. Find the angle θ associated with each sine value. 1. θ = sin - 1 (0)= ____________ 2. θ = sin - 1 (1 / 2) = __________ 3. θ = sin - 1 ( - 1) = ____________ 4. θ = sin - 1 ( 2 / 2) = _________ 5. θ = sin - 1 ( - 1 / 2) = __________ 6. θ = sin - 1 ( - 3 / 2) = _________ Section 4.7 Inverse Trigonometric Functions, Page 3 -1.0 -0.5 0.5 1.0 -π/2 -π/4 π/4 π/2

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1 -1 1 -1 Section 4.7 Inverse Trigonometric Functions, Page 4 2) Objective 2:
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Section 4.7 handout ann_1 - Section 4.7 Inverse...

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