Evaluating Inverse Trig Functions or.

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Presentation transcript:

Evaluating Inverse Trig Functions or

Given The Function Find The Angle

In The Coordinate Plane

Degrees

Review The Unit Circle

Determine the value of angle , where Example 1 Determine the value of angle , where Degrees

Wrong Polarity

Wrong Polarity

Why?

is called the Reference Angle

is called the Reference Angle

is called the Reference Angle

SAME Reference Angle and SAME Polarity

Degrees

Make sure you calculator is in Degrees. Check MODE

There Should Be Two Answers! Where's The Other Angle? There Should Be Two Answers!

Let's Look at FUNCTIONS and INVERSE FUNCTIONS

? Inverse INVERSE NOT A FUNCTION

An Angle in Quadrant I only The Calculator Gives You An Angle in Quadrant I only You Find The Other One SAME Reference Angle SAME Polarity

Determine the value of angle , where Example 2 Determine the value of angle , where Degrees

Using The Unit Circle

Wrong Polarity

Wrong Polarity

SAME Reference Angle and SAME Polarity

What's Up With This?

A Negative Angle in Quadrant IV only The Calculator Gives You A Negative Angle in Quadrant IV only Convert To Positive Coterminal Angle You Find The Other One SAME Reference Angle SAME Polarity

GENERAL INSTRUCTIONS

Draw the Angle in correct Quadrant To Find Take What The Calculator Gives You Draw the Angle in correct Quadrant Convert To A Positive Coterminal Angle If Necessary Label the Reference Angle Draw The Other One SAME Reference Angle SAME Polarity Determine It's Measure

QUADRANT TABLE Function Polarity 2nd Angle sin cos

QUADRANT TABLE Function Polarity 2nd Angle sin + cos ?

QUADRANT TABLE Function Polarity 2nd Angle sin + I cos ?

QUADRANT TABLE Function Polarity 2nd Angle sin + I II cos

QUADRANT TABLE Function Polarity 2nd Angle sin + I II – cos ?

+ – sin cos QUADRANT TABLE I II IV It will be a negative angle Function Polarity 2nd Angle sin + I II – IV cos It will be a negative angle Must be converted to a positive coterminal angle

QUADRANT TABLE Function Polarity 2nd Angle sin + I II – IV cos ?

QUADRANT TABLE Function Polarity 2nd Angle sin + I II – IV III cos

QUADRANT TABLE Function Polarity 2nd Angle sin + I II – IV III cos ?

QUADRANT TABLE Function Polarity 2nd Angle sin + I II – IV III cos ?

QUADRANT TABLE Function Polarity 2nd Angle sin + I II – IV III cos

QUADRANT TABLE Function Polarity 2nd Angle sin + I II – IV III cos ?

QUADRANT TABLE Function Polarity 2nd Angle sin + I II – IV III cos ?

QUADRANT TABLE Function Polarity 2nd Angle sin + I II – IV III cos

What About The Tangent?

QUADRANT TABLE Function Polarity 2nd Angle tan + –

QUADRANT TABLE Function Polarity 2nd Angle tan + I –

QUADRANT TABLE Function Polarity 2nd Angle tan + I III –

+ – tan QUADRANT TABLE I III IV It will be a negative angle Function Polarity 2nd Angle tan + I III – IV It will be a negative angle Must be converted to a positive coterminal angle

QUADRANT TABLE Function Polarity 2nd Angle tan + I III – IV II

Example 1

Round to nearest tenth of a degree.

? negative ? ?

?

Example 2

Round to nearest tenth of a degree.

positive ?

?

Example 3

Round to nearest tenth of a degree.

positive ?

?

Example 4

Round to nearest tenth of a degree.

?

?

? negative

?

Example 5

Round to nearest tenth of a degree.

positive ?

?

Example 6

Round to nearest tenth of a degree.

?

?

? negative

?

What About

Finish The Problem Like Example 3 Given then Finish The Problem Like Example 3

Given

NEXT

Finish The Problem Like Example 1 Given then Finish The Problem Like Example 1

Given then

NEXT

Finish The Problem Like Given then Example 6 Finish The Problem Like

Given then