1. Trigonometric Functions
Chapter 11
Trigonometric Functions
11. Trigonometric Functions
11.1 Trigonometric Ratios and General Angles
11.2 Trigonometric Ratios of Any Angles
11.3 Graphs of Sine, Cosine and Tangent Functions
11.3 Graphs of Sine, Cosine and Tangent Functions

2. Trigonometric Equations
11.3 Graphs of Sine, Cosine and Tangent Functions
Objectives
In this lesson, we will learn
about the amplitude, period and symmetry of the sine and cosine
functions,
to sketch the graphs of y = a sin (bx) + c, y = a sin (x ÷ b) + c,
y = a cos (bx) + c, y = a sin (x ÷ b) + c and y = a tan (bx). (where a and b
are positive integers and c is an integer.)
to state the principal values of sin–1 y, cos–1 y and tan–1 y.
11.3 Graphs of Sine, Cosine and Tangent Functions
Objectives
In this lesson we will learn about the amplitude, period and symmetry of the sine and cosine functions. We will sketch the graphs of y = a sin (bx) + c,
y = a sin (x ÷ b) + c, y = a cos (bx) + c, y = a sin (x ÷ b) + c and y = a tan (bx). (Where a and b are positive integers and c is an integer.) We will also learn to state the principal values of sin–1 y, cos–1 y and tan–1 y.

3. Trigonometric Equations
Graph of the Sine Function
Signs of Trigonometric Ratios in Quadrants

4. Trigonometric Equations
Graph of the Cosine Function
Graph of the Cosine Function

5. Trigonometric Equations
Graph of the Tangent Function
Graph of the Tangent Function

6. Trigonometric Equations
Principal Values
The principal values of the trigonometric function always include one complete cycle.
Principal Values

7. Trigonometric Equations
Amplitude and Period
Period = 360°
Amplitude = 1
Period = 360°
Amplitude and Period
Amplitude = 1
Period = 180°

8. Trigonometric Equations
Exercise 11.3, qn 3(b)
State the amplitude and period of y and sketch the graph in the given interval.
The coefficient of sin x
The amplitude is 2.
Divide 360° by the coefficient of x.
Page 245, Exercise 11.3, Question 3 (b)
The period is 360° ÷ 3
= 120°

9. Trigonometric Equations
Exercise 11.3, qn 3(g)
State the amplitude and period of y and sketch the graph in the
given interval.
The coefficient of cos x
The amplitude is 6.
Page 245, Exercise 11.3, Question 3 (g)
Divide 2π by the coefficient of x.
The period is

10. Trigonometric Equations
Exercise 11.3, qn 4(b)
Sketch the graph of y in the given interval.
Sketch
Reflect the negative portion in the x-axis.
Page 245, Exercise 11.3, Question 4 (b)