4.7 Inverse Trigonometric functions

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Presentation transcript:

4.7 Inverse Trigonometric functions Arcsine Arccosine

Lets review inverse functions Find the inverse of f(x) = 3x + 6 y = 3x + 6 Inverse functions switch domain and range. So, x = 3y + 6 ( solve for y) x – 6 = 3y ⅓ x – 2 = y f -1(x) = ⅓ x - 2

What is the domain and range of the Sine function Domain: All real numbers Range: - 1 to 1

What is the domain and range of the Inverse of the Sine function The inverse’s Domain would be -1 to 1; Yet the Range is not all real numbers. Range

Inverse of the Cosine Domain: [ -1,1] Range:

The Tangent function Domain: All real numbers except Where n is a integer Range: All real numbers

Inverse of Tangent function Domain: All real numbers Range:

Definition of Arcsine The arc sine is the inverse function of the sine. What is the angle that has a sine equal to a given number Since,

Solve Find the exact value. For these problems All answers are in the First Quadrant.

Solve Find the exact value. For these problems All answers are in the First Quadrant.

Do you remember? What are the answers

Solve Be careful to make sure it is in the Range

Solve Be careful to make sure it is in the Range

For the arccos the range is So

Solve using a triangle Cot(arctan x) Let arctan x = u Cot u =

Solve Let

Solve So

Show that

Show that Using arccos

Show that Using arccos

Homework Page 328 – 331 # 1, 5, 9, 13, 16, 21, 27, 33, 40, 44, 51, 61, 66, 74, 85, 94, 104, 110, 122

Homework Page 328 – 331 # 3, 8, 12, 15, 18, 24, 30, 37, 41, 47, 56, 65, 71, 83, 91, 96, 107, 121