Warm Up1.Solve 𝑐𝑜𝑡2𝜃 = 4 for 0° ≤ 𝜃 ≤ 360°

2.Handout - 6 Multiple Choice Problems

26.6°, 𝟏𝟓𝟑. 𝟒°, 𝟐𝟎𝟔. 𝟔°, 𝟑𝟑𝟑. 𝟒°

2, 2, 3, 2, 1, 1

Objectives: To solve trig equations

To graph trig equations

Solve for0 ≤ 𝑥 < 2𝜋

1. 6𝑠𝑖𝑛2𝑥 = 5

2. 5𝑠𝑖𝑛3𝑥 = −2

Solve the equation 6sin 2 5, 0 2 .

Give answers to the nearest hundredth of a radian.

x x

6sin 2 5

5sin 2

6

0 2 0 2 4

2 0.985, 0.985 2.157, 2 0.985 7.27, 2 2.157 8.44

0.49, 1.08, 3.63, 4.22

x

x

x x

x

x

x

y

Solve the equation 6sin 2 5,

0 2 , with a calculator.

x

x

Solve: 5𝑠𝑖𝑛3𝑥 = −2for 0 ≤ 𝑥 < 2𝜋

1.18, 1.96, 3.28, 4.05, 5.37, 6.15

𝑦 =𝑎𝑠𝑖𝑛𝑏 𝑥 − ℎ + 𝑘𝑎𝑐𝑜𝑠𝑏 𝑥 − ℎ + 𝑘

Phase Shift(𝑥 − ℎ) goes right(𝑥 + ℎ) goes left

Vertical Shift+𝑘 goes up

−𝑘 goes down

Reflection𝑎 < 0 reflects x-axis𝑏 < 0 reflects y-axis

VerticalStretch/Shrink

Amplitude = 𝑎

Horizontal Stretch/Shrink

Period = 2𝜋

𝑏

Axis of the wave (k):

𝑦 =𝑀𝑎𝑥 𝑦 +min𝑦

2

𝑎𝑠𝑖𝑛𝑏 𝑥 − ℎ + 𝑘

is the same as𝑎𝑠𝑖𝑛 𝑏𝑥 − 𝑏ℎ + 𝑘

b = 2𝜋

𝑝𝑒𝑟𝑖𝑜𝑑

𝑎 =𝑀𝑎𝑥 𝑦 −min 𝑦

2

ClassworkWorksheet

Translation of a Sine Function

xy sin

2

2

3 2

1

1

1AmplitudePeriod

2

11

Translation of a Sine Function

siny

2

2

3 2

1

1

1AmplitudePeriod

2

2

x

2

xx

Graphing a Vertical Translation

Graph the function.

xy cos2 .1

2

2

3 2

1

3

1Amplitude

Period 2

Translation

down 2

Graphing a Vertical Translation

Graph the function.

xy sin3 .2

2

2

3 2

4

2

1Amplitude

Period 2

Translation

up 3

Graphing a Horizontal Translation

Graph the function.

xy sin .3

2

2

3

1

1

Amplitude

Period

Translation

right

2

1

2

Graphing a Horizontal Translation

Graph the function.

xy cos .4

2

2

3

1

1

Amplitude

Period

Translation

left

2

1

2

Graphing a Horizontal Translation

Graph the function.

2cos3 .5

xy

2

2

3

3

3

Amplitude

Period

Translation

right /2

2

3

2