6.4 Inverses of the Trigonometric FunctionsJan 5

Do NowSolve for x

1) Sin x = -1/2

2) Tan x = 1

Quiz Review

• Retakes by?

Inverse Trig Functions

• Recall: how to find inverse functions (switch x and y)

• Problem: If we switch x and y, the inverse fails the vertical line test

• (Draw picture here)

Inverse Trig Functions

• The 3 inverse trig functions (other 3 are reciprocals):

• 1)

• 2)

• 3)

Domain an Range

• To make these functions, we need to restrict the domain and range

Domain Range

[-1, 1]

[-1, 1]

Evaluating Inverse Trig Functions

• When evaluating these functions, we want to find the angle that results in the value.

• Note: because of the restriction in the ranges, we can only consider angles in each range

ex

• Find each of the following function values• 1)

• 2)

• 3)

Calculators

• Calculators can be used to find inverse trig values

• Inverse sin,cos,tan – buttons

• Inverse reciprocals – your input will be the reciprocal

Ex

• Approximate using a calculator • 1)

• 2)

• 3)

Closure

• Evaluate in radians and degrees

• HW: p.575 #1-35 odds

6.4 Inverse Trig FunctionsTues Jan 6

• Do Now• Evaluate in radians and degrees• 1)

• 2)

HW Review: p.575 #1-35

Composition of Trig and Inverse Functions

• When evaluating a composition of trig and inverse trig values, compute the ‘inside’ first.

• Keep in mind the domain and range of each composition

Ex1

• Simplify

Ex2

• Simplify

Ex3

• Simplify

Ex4

• Simplify

Ex5

• Simplify

Ex6

• Simplify

Simplifying Compositions with X

• When simplifying a composition with a variable, draw a right triangle with an angle that has the given ratio

Ex

• Find

Ex

• Evaluate

Closure

• Evaluate

• HW: p.575 #37-67 odds