Everything Maths Grade 10

Period

The period ofy=asin+qis 360 °. This means that one sine wave is completed in 360 °.

Intercepts

They-intercept off() =asin+qis simply the value off()at= 0°

y=f(0°)

=asin 0 °+q

=a(0) +q

=q

This gives the point(0;q)

Important:when sketching trigonometric graphs, always start with the basic graph and then consider the effects
ofaandq.

Worked example 17: Sketching a sine graph

QUESTION

Sketch the graph off() = 2sin+ 3for 2 [0°; 360°].

SOLUTION

Step 1: Examine the standard form of the equation

From the equation we see thata > 1 so the graph is stretched vertically. We also see thatq > 0 so the graph is

shifted vertically upwards by 3 units.

Step 2: Substitute values for

 0 ° 30 ° 60 ° 90 ° 120 ° 150 ° 180 ° 210 ° 240 ° 270 ° 300 ° 330 ° 360 °

f() 3 4 4,73 5 4,73 4 3 2 1,27 1 1,27 2 3

Step 3: Plot the points and join with a smooth curve

30 ◦ 60 ◦ 90 ◦ 120 ◦ 150 ◦ 180 ◦ 210 ◦ 220 ◦ 270 ◦ 300 ◦ 330 ◦ 360 ◦

1

2

3

4

5

f() = 2sin+ 3



f()

Domain:[0°; 360°]Range:[1; 5]

x-intercepts: noney-intercepts:(0°; 3)

Maximum turning point:(90°; 5)Minimum turning point:(270°; 1)

Chapter 6. Functions 191