Everything Maths Grade 10

Effect ofa

a > 1 : vertical stretch, amplitude

increases



y

a= 0

a> 1

0 <a< 1

 1 <a< 0

a< 1

a= 1: basic cosine graph

0 < a < 1 : amplitude decreases

 1 < a < 0 : reflection aboutx-

axis, amplitude decreases

a < 1 : reflection aboutx-axis,

amplitude increases

Table 6.8:The effect ofaon a cosine graph.

Effect ofq

q > 0 : vertical shift upwards byq

units



y

q= 1

q> 0

q< 0

q= 0: basic cosine graph

q < 0 : vertical shift downwards

byqunits

Table 6.9:The effect ofqon a cosine graph.

Discovering the characteristics EMA5B

Domain and range
Forf() =acos+q, the domain is[0°; 360°]

It is easy to see that the range off()will be the same as the range ofasin+q. This is because the maximum
and minimum values ofacos+qwill be the same as the maximum and minimum values ofasin+q.

Fora > 0 the range off() =acos+qisff() :f() 2 [a+q;a+q]g

Fora < 0 the range off() =acos+qisff() :f() 2 [a+q;a+q]g

Period

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

Intercepts

They-intercept off() =acos+qis calculated in the same way as for sine.

194 6.6. Trigonometric functions