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

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Presentation on theme: "Math III Accelerated Chapter 14 Trigonometric Graphs, Identities, and Equations 1."— Presentation transcript:

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

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

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

4 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

5 Examples of Periodic Functions 5

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

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

8 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

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

10 Example 1  Graph y = 2 sin x 10

11 Example 2  Graph y = sin 4 x 11

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

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

14 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

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

16 Example 3  Graph 16

17 Example 4  Graph y = –3 cos x 17

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

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

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

21 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

22 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

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

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

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

26 Homework 14.1  Practice 14.1 26


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