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Chp 4.7 Inverse Trigonometry Functions (pg. 343) Standard: Algebra 2 Standard: F.TF.2.1 Bellwork Sketch the graph of the following functions. 1. y = βtan 2x 2. y = sec(3x β π) + 2 Objective: To graph inverse trigonometric functions. Inverse Sine The inverse sine function is defined by: Function y = arcsin x if and only if sin y = x Domain: [β1, 1] π π Range: [β , 2 2 ] Inverse Cosine The inverse cosine function is defined by: Function y = arccos x if and only if cos y = x Domain: [β1, 1] Range: [0, π] Inverse The inverse tangent function is defined by: Tangent Function y = arctan x if and only if tan y = x Domain: (ββ, β) π π Range: [β , 2 2 ] Example 1 If possible, find the exact values. a. 1 β3 b. π ππβ1 2 ππππ ππ β 2 c. π ππβ1 2 Example 2/3 Find the exact value. a. β2 ππππππ 2 b. πππ β1 (β1) c. arctan 0 d. π‘ππβ1 (β1) Example 4 Use a calculator to approximate the value. a. arctan(β8.45) b. sin-1 0.2247 c. arccos 2 Inverse If β1 β€ x β€ 1 and β πβ€ y β€ π, then 2 2 Properties of Trig. Function sin(arcsin x) = x and arcsin(sin y) = y If β1 β€ x β€ 1 and 0 β€ y β€ Ο, then cos(arccos x) = x and arccos(cos y) = y If x is a real number and β π 2 π < y < , then 2 tan(arctan x) = x and arctan(tan y) = y. Example 5 If possible, find the exact values. a. tan[arctan(β5)] 5π b. arcsinβ‘(π ππ 3 ) c. cos(cos-1π)