Lesson Worksheet 6.2(I) Objective: To recognize the graphs and the properties of trigonometric functions. Graphs of trigonometric functions

Name: ____________________ ( ) Class: Date:

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Lesson Worksheet 6.2(I)

Objective: To recognize the graphs and the properties of trigonometric functions.

Graphs of trigonometric functions y = sin x, y = cos x and y = tan x for 0º  x  360º:

y = sin x y = cos x y = tan x

1. Using the above graphs, complete the following table for 0º  x  360º.

y = sin x y = cos x y = tan x

(a) Maximum value /

(b) Minimum value /

(c) x-intercepts

(d) Period 360º 360º

2. The figure shows the graph of the trigonometric function y = sin 3x for 0º  x  240º. Exercise 6.2: 1 – 4

(a) The maximum value of y = sin 3x is . (b) The minimum value of y = sin 3x is . (c) The period of y = sin 3x is .

3. Find the maximum and minimum values of 4 sin x algebraically.

Chapter 6

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4. Find the maximum and minimum values of (3 + 2 cos x) algebraically.

5. Find the maximum and minimum values of (5 sin x – 1) algebraically.

6. Find the maximum and minimum values of cos² x algebraically. Exercise 6.2: 5 – 10

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7. Find the maximum and minimum values of (4 + 3 sin² x) algebraically.

For –1  cos x  1, 1² =

0² = (–1)² =

Name: ____________________ ( ) Class: Date:

48 © Educational Publishing House Ltd

Lesson Worksheet 6.2(II)

Objective: To recognize the graphs and the properties of trigonometric functions.

Graphs of trigonometric functions y = sin x, y = cos x and y = tan x for 0º  x  360º:

y = sin x y = cos x y = tan x

1. Using the above graphs, complete the following table for 0º  x  360º.

y = sin x y = cos x y = tan x

(a) Maximum value /

(b) Minimum value /

(c) x-intercepts

(d) Period 360º 360º

2. The figure shows the graph of the trigonometric function y = cos 3x for 0º  x  240º. Exercise 6.2: 1 – 4

(a) The maximum value of y = cos 3x is . (b) The minimum value of y = cos 3x is . (c) The period of y = cos 3x is .

3. Find the maximum and minimum values of 5 sin x algebraically.

Chapter 6

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4. Find the maximum and minimum values of (4 + 3 cos x) algebraically.

5. Find the maximum and minimum values of (2 sin x – 7) algebraically.

6. Find the maximum and minimum values of cos² x algebraically. Exercise 6.2: 5 – 10

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Find the maximum and minimum values of each of the following trigonometric functions algebraically. (7 – 8)

7. y = 6 + sin² x 8. y = 2 – cos x