6.4 Inverses of the Trigonometric Functions Jan 5 Do Now Solve for x 1)Sin x = -1/2 2)Tan x = 1.

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Presentation transcript:

6.4 Inverses of the Trigonometric Functions Jan 5 Do Now Solve 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 DomainRange [-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 Functions Tues 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