Everything Maths Grade 10

Comparison of graphs ofy=sinandy=cos EMA5C

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

 1

1

y=cos

y=sin



y

Notice that the two graphs look very similar. Both waves move up and down along thex-axis. The distances
between the peaks for each graph is the same. The height of the peaks and the depths of the troughs are also
the same.

If you shift the whole cosine graph to the right by 90 °it will overlap perfectly with the sine graph. If you shift
the sine graph 90 °to the left it would overlap perfectly with the cosine graph. This means that:

sin =cos( 90 °) (shift the cosine graph to the right)

cos =sin(+ 90°) (shift the sine graph to the left)

Tangent function EMA5D

Functions of the formy=tan EMA5F

Worked example 20: Plotting a tangent graph

QUESTION

y=f() =tan [0° 360 °]

Use your calculator to complete the following table.

Choose an appropriate scale and plot the values withon thex-axis andtanon they-axis. Round your

answers to 2 decimal places.

 0 ° 30 ° 45 ° 60 ° 90 ° 120 ° 135 ° 150 ° 180 °

tan

 210 ° 235 ° 240 ° 270 ° 300 ° 315 ° 330 ° 360 °

tan

SOLUTION

Step 1: Substitute values for

 0 ° 30 ° 45 ° 60 ° 90 ° 120 ° 135 ° 150 ° 180 °

tan 0 0,58 1 1,73 undef 1,73  1 0,58 0

 210 ° 235 ° 240 ° 270 ° 300 ° 315 ° 330 ° 360 °

tan 0,58 1 1,73 undef 1,73  1 0,58 0

196 6.6. Trigonometric functions