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Math III Accelerated Chapter 14 Trigonometric Graphs, Identities, and Equations 1

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Warm Up 14.1 Find the sine, cosine, and tangent for each. 2

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14.1 Graph Sine, Cosine, and Tangent Functions Objective: Graph sine, cosine, and tangent functions. 3

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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. 4

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Examples of Periodic Functions 5

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Sine Create a table of values for y = sin x & graph. 6

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Graph of y = sin x Domain:Range: Period:Amplitude: Max:Min: Zeros: 7

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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 = 8

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Graph y = sin x By Hand Use five key points in one period: Zero, Max, Zero, Min, Zero 9

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Example 1 Graph y = 2 sin x 10

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Example 2 Graph y = sin 4 x 11

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Cosine Create a table of values for y = cos x & graph. 12

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Graph of y = cos x Domain:Range: Period:Amplitude: Max:Min: Zeros: 13

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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 = 14

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Graph y = cos x By Hand Use five key points in one period: Max, Zero, Min, Zero, Max 15

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Example 3 Graph 16

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Example 4 Graph y = –3 cos x 17

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Example 5 (NTG Ex. 2) Write a sine function with an amplitude of 3 and a frequency of 1000. 18

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Tangent Create a table of values for y = tan x & graph. 19

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Graph of y = tan x Domain: Range: Period: Zeros: VAs: 20

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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 = 21

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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 22

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Example 6 (NTG Ex. 3 ) Graph one period of the function y = 2 tan x. 23

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Example 7 (NTG CP 5 ) Graph one period of the function y = tan 4 x. 24

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Example 8 (NTG CP 6) Graph one period of the function y = tan π x. 25

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Homework 14.1 Practice 14.1 26

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