Use your knowledge of UC to find the values of .

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Presentation transcript:

Use your knowledge of UC to find the values of 

Section 7-6 The Inverse Trigonometric Functions Objective: To find values of the inverse trigonometric functions.

Reminder about reference angles

REVIEW CONCEPTS:

review  One to one function  Restricted domain  Inverse functions –Inverse function equations algebraically. –Inverse functions graphically.

Trig FUNCTIONS  Sine, cosine and tangent are all functions.  Are they all one-to-one functions?

Notice how the axes are scaled!

Trig functions Does tan θ have an inverse that is a function? Justify your answer. If you answered no, you are right. However, we need to have a way to “undo” tan θ.

The graph does not have an inverse function.

Inverse of trig functions Restrict domain to f(x)=Tan x Inverse function is Tan -1 x Notice T is capitalized

Tan x has an inverse. Notice how the axes are scaled!

Sec 7.6 Warm Up Day 2

Notice how the axes are scaled!

Inverse of trig functions

Notice how the axes are scaled!

Inverse of trig functions Restrict domain to 0 <x <  F(x)=Cos x Inverse function is Cos -1 x

Notice how the axes are scaled!

graphs of trig functions graph of inverse funtions

Restricted domains summarized: Notice the restricted domain for each of the inverse functions includes the first quadrant… i.e. the reference angle.

Sine Function: sin(30°) = 0.5 Inverse Sine: Sin -1 (0.5) = 30°

 tan(angle value)= ratio  Tan -1 (ratio)= angle value  sin(angle value)= ratio  Sin -1 (ratio)= angle value  cos(angle value)= ratio  Cos -1 (ratio)= angle value

Example 1  Find Tan -1 2 with a calculator. 0<θ<360°  First make sure your calculator is in the correct mode.

Example 2  Find Tan -1 (-1) without a calculator. 0<θ<2 

Restricted domains summarized:

Use your knowledge UC and RA:

Warm UP Day 2: :

Parent graph: sine function

review graphing:  Study the graphs below. Draw inverse of each graph.

Example 3  A.) Find Sin -1 (-0.8) with a calculator. 0<θ<360°  B.) Find Cos -1 (-0.5) without a calculator. 0<θ<2 

Example 4 Hint: pay attention to restricted domain. A) Find the value of the above expression without a calculator.

Example 4 Hint: pay attention to restricted domain. B) Find the value of with a calculator.

No matter the mode setting is…

Homework  Sec 7.6 written exercises  Day 1: #1-9 All, read #10  Day 2: #11-21 All

Review ction_5_1.html