H PRECALC Lesson 89 Reference Angles between 0 and 360.notebook

Lesson 89 FINDING AND USING

Multiples of 45

April 24, 2018

o

REFERENCE ANGLES (in degrees) o

0 < Θ < 360

o

HW 89

Differentiating angles and values 4 circles on side board and trig values

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H PRECALC Lesson 89 Reference Angles between 0 and 360.notebook

April 24, 2018

Calc in degree mode

Trig Values that are Positive

y1 = sinx

II

I

y2 = cosx y3 = tanx

all

sin (and csc)

TBL SET

ALL

STUDENTS

TBL Start 0 Tbl = 15

TAKE

Indep Auto

CALCULUS

tan (and cot)

cos (and sec)

III

IV

Every angle, except for quadrantal angles have Reference Angles, RA. RA are always acute.

Set up your notes like this...

A RA is the angle you "refer" to when trying to find trig values for the given angle, θ.

Method I

Method II

θ and its reference angle have the same trig values, except that the signs may differ. o

o

For example θ = 330 has a reference angle, RA = 30 Check your unit circle and find: o

sin 330 =

o

sin 30 =

o

cos 30 =

o

tan 30 =

cos 330 = tan 330 =

Examples

o

o

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H PRECALC Lesson 89 Reference Angles between 0 and 360.notebook

There are two ways to find θ's reference angle:

April 24, 2018

Method 2: Using RA formulas To find the measure of the reference angle (RA) for a

Method 1: "Graphing"

positive angle, Θ, between 0 and 360 (not including

1. Sketch a circle and graph θ in standard position.

quadrantal angles):

2. Drop a vertical line from the point where the terminal

1. Determine the quadrant the terminal side is in

side "hits" the circle to the x-axis, forming a right triangle.

2. Use the formula in that quadrant.

II

3. The reference angle, RA, will be the acute central angle.

RA = Θ

RA = Θ -180

RA = 360 - Θ

III

o

Ex 1. Find the reference angle θ = 30 .

Method I

Method II

I

RA = 180 - Θ

Write on side board.

IV

o

Ex 2. Find the reference angle θ = 135 .

Method I

Method II

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H PRECALC Lesson 89 Reference Angles between 0 and 360.notebook

o

Ex 3. Find the reference angle θ = 300 .

Method I

Method II

o

Ex 5. Find the reference angle θ = 60 .

Method I

Method II

April 24, 2018

o

Ex 4. Find the reference angle θ = 225 .

Method I

Method II

o

Ex 6. Find the reference angle θ = 150 .

Method I

Method II

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H PRECALC Lesson 89 Reference Angles between 0 and 360.notebook

April 24, 2018

Ex 7. Find the following using RAs:

How to use RAs to find trig values for θ. 1. Make box for your answer after the problem.

θ's

2. Identify θ.

Find Trig

3. Sketch θ and label the quadrant in which the terminal side lies.

Function

Trig Value

Terminal θ =

Sketch θ

Value for θ

Side in

RA

of RA (from card)

Quadrant ___

4. Find θ's RA (Method I or II). 5. "Find" the trig value of the RA (don't use your calc; you

sin 120

o

might want to record sin, cos or tan first when finding csc, cos 210

sec or cot).

o

6. Adjust the sign (+ or -) of the trig value based on the quadrant and write your answer in the box; all answers

tan -135

o

should be exact and rationalized.

Ex 8. Find the following using RAs:

Ex 9. Find the following using RAs:

θ's Function Value for θ

θ's

Terminal

Find Trig θ =

Sketch θ

Side in Quadrant

RA

Trig Value

Find Trig

of RA

Function

(from card)

Value for θ

___

sin -45

o

cos 240

tan 150

Terminal θ =

Sketch θ

Side in Quadrant

Trig Value RA

of RA (from card)

___

o

csc 315

o

o

cot 60

o

sec 225

o

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H PRECALC Lesson 89 Reference Angles between 0 and 360.notebook

April 24, 2018

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