Everything Maths Grade 10

y=f(0°)

=acos 0 °+q

=a(1) +q

=a+q

This gives the point(0°;a+q).

Worked example 19: Sketching a cosine graph

QUESTION

Sketch the graph off() = 2cos+ 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() 5 4,73 4 3 2 1,27 1 1,27 2 3 4 4,73 5

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() = 2cos+ 3



f()

Domain:[0°; 360°]Range:[1; 5]

x-intercepts: noney-intercept:(0°; 5)

Maximum turning points:(0°; 5),(360°; 5)Minimum turning point:(180°; 1)

Chapter 6. Functions 195