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

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.

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

Trigonometric Equations Graph of the Cosine Function Graph of the Cosine Function

Trigonometric Equations Graph of the Tangent Function Graph of the Tangent Function

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

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

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°

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

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)