Everything Maths Grade 10

On the same set of axes, plot the following graphs for 0 ° 360 °:

1.y 6 = 2 tan

2.y 7 =tan

3.y 8 =tan

4.y 9 = 2tan

Use your results to deduce the effect ofa.

The effect ofq

The effect ofqis called a vertical shift because the whole tangent graph shifts up or down byqunits.

• Forq > 0 , the graph is shifted vertically upwards byqunits.


• Forq < 0 , the graph is shifted vertically downwards byqunits.

The effect ofa

The value ofaaffects the steepness of each of the branches of the graph. The greater the value ofa, the quicker
the branches of the graph approach the asymptotes.

a < 0 a > 0

q > 0

0 x

y

0 x

y

q= 0

0 x

y

0 x

y

q < 0

0 x

y

0 x

y

Table 6.10:The effect ofaandqon a tangent graph.

198 6.6. Trigonometric functions