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**Chapter 14 Trigonometric Graphs, Identities, and Equations**

Math III Accelerated Chapter 14 Trigonometric Graphs, Identities, and Equations

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Warm Up 14.1 Find the sine, cosine, and tangent for each.

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**14.1 Graph Sine, Cosine, and Tangent Functions**

Objective: Graph sine, cosine, and tangent functions.

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Periodic Function A function is periodic if it repeats at regular intervals. A cycle is the shortest repeating portion. The period is the horizontal length of one cycle. The amplitude is one-half the difference of the maximum, M and the minimum, m.

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**Examples of Periodic Functions**

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**Sine Create a table of values for y = sin x & graph. x 0° 30° 45° 60°**

90° 135° 180° 270° 360° sin x

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Graph of y = sin x Domain: Range: Period: Amplitude: Max: Min: Zeros:

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**Sine Function The function y = sin x is the parent function.**

A simplified version of the general equation for sine is where |a| = amplitude b = number of cycles in one period That is, period =

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**Graph y = sin x By Hand Use five key points in one period:**

Zero, Max, Zero, Min, Zero

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Example 1 Graph y = 2 sin x

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Example 2 Graph y = sin 4x

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Cosine Create a table of values for y = cos x & graph. x π 2π cos x

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Graph of y = cos x Domain: Range: Period: Amplitude: Max: Min: Zeros:

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**Cosine Function The function y = cos x is the parent function.**

A simplified version of the general equation for cosine is where |a| = amplitude b = number of cycles in one period That is, period =

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**Graph y = cos x By Hand Use five key points in one period:**

Max, Zero, Min, Zero, Max

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Example 3 Graph

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Example 4 Graph y = –3 cos x

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Example 5 (NTG Ex. 2) Write a sine function with an amplitude of 3 and a frequency of 1000.

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**Tangent Create a table of values for y = tan x & graph. x –1.57 –1.5**

1.5 1.57 tan x

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Graph of y = tan x Domain: Range: Period: Zeros: VAs:

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**Tangent Function The function y = tan x is the parent function.**

The simplified version of the general equation for tangent is where b = number of cycles in one period That is, period =

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**Graph y = tan x By Hand Find the VAs Solve for x: and .**

Period is distance between VAs. Find the zero Midway between the VAs

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Example 6 (NTG Ex. 3) Graph one period of the function y = 2 tan x.

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Example 7 (NTG CP 5) Graph one period of the function y = tan 4x.

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Example 8 (NTG CP 6) Graph one period of the function y = tan πx.

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Homework 14.1 Practice 14.1

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Aim: What are the graphs of tangent function and reciprocal functions?

Aim: What are the graphs of tangent function and reciprocal functions?

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