13.4 & 13.5 The Sine & Cosine FunctionsObjectives:

1. To identify properties of the sine function.

2. To graph and write sine functions.

3. To graph and write cosine functions.

Sine Graph

Period: Amplitude:

Max: Min:

Domain: Range:

Cosine Graph

Period: Amplitude:

Max: Min:

Domain: Range:

Sine General Formula

𝑦=𝑎 sin𝑏𝜃Cosine General Formula

𝑦=𝑎 cos𝑏𝜃• Multiplying a number in front () changes

the amplitude.• amplitude

• Multiplying a number inside () changes the period.• To get new multiply by the reciprocal of

• period

Example 1: Graph

Example 2: Graph

1. Which musical based on Romeo & Juliet was a 60s Oscar winner?

Twister

Trivia…

2. What 1996 movie was hyped with the line: "It Will Blow Audiences Right Out of the Theater"?

West Side Story

3. What was Will Smith’s first acting job?

Fresh Prince of Belair

Example 3: Graph

Example 4: Graph

Homework: 13.4

P 738 – 739: 13, 15, 17, 18, 19, 23, 27-30 13.5

P 746 – 747: 1, 3, 5, 7, 13, 25, 27

13.6 The Tangent FunctionObjectives:

1. To graph the tangent function.

Tangent Graph

Period: Period:

Dotted Lines: Vertical Asymptotes

(where tangent is undefined)

One Cycle: Occurs between

Example 1: Given find:

a) Period:

b) Interval which cycle occurs:

c) Equation for vertical asymptote:

Example2: Sketch two cycles of the graph

Homework P 752: 11, 13, Graph &