Everything Maths Grade 10

Cosine function EMA57

Functions of the formy=cos EMA58

Worked example 18: Plotting a cosine graph

QUESTION

y=f() =cos [0° 360 °]

Use your calculator to complete the following table.

Choose an appropriate scale and plot the values ofon thex-axis andcoson they-axis. Round your answers

to 2 decimal places.

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

cos

SOLUTION

Step 1: Substitute values for

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

cos 1 0,87 0,5 0 0,5 0,87  1 0,87 0,5 0 0,5 0,87 1

Step 2: Plot the points and join with a smooth curve

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

 1

1



y

Notice the similar wave shape of the graph. The period is also 360 °and the amplitude is 1. The maximum

value ofy=cosis 1 and the minimum value is1.

Domain:[0°; 360°]Range:[1; 1]

x-intercepts:(90°; 0),(270°; 0)y-intercepts:(0°; 1)

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

192 6.6. Trigonometric functions