Everything Maths Grade 10

Effect ofa

a > 1 : vertical stretch, amplitude

increases



y

a= 1

a> 1

0 <a< 1

 1 <a< 0

a< 1

a= 1: basic sine graph

0 < a < 1 : vertical contraction,

amplitude decreases

 1 < a < 0 : reflection aboutx-

axis of 0 < a < 1

a < 1 : reflection aboutx-axis

ofa > 1

Table 6.6:The effect ofaon a sine graph.

Effect ofq

q > 0 : vertical shift upwards byq

units



y

q=0

q> 0

q< 0

q= 0: basic sine graph

q < 0 : vertical shift downwards

byqunits

Table 6.7:The effect ofqon a sine graph.

Discovering the characteristics EMA56

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

The range off() =asin+qdepends on the values ofaandq.

Fora > 0 :

 1 sin 1

aasina

a+qasin+qa+q

a+qf()a+q

For all values of,f()is always betweena+qanda+q.

Therefore fora > 0 , the range off() =asin+qisff() :f() 2 [a+q; a+q]g

Similarly, fora < 0 , the range off() =asin+qisff() :f() 2 [a+q;a+q]g

190 6.6. Trigonometric functions