3.The graph below shows a trigonometric equation of the following form:y=acos+q. Two points
are shown on the graph:Point Aat(180◦;1,5), andPoint B:(0◦;0,5). Calculate the values ofa(the
amplitude of the graph) andq(the vertical shift of the graph).
30 60 90 120 150 180 210 240 270 300 330 360
3
2
1
1
B
A
x
y
4.The graph below shows a trigonometric equation of the following form:y=acos+q. Two points
are shown on the graph:Point Aat(90◦;0,0), andPoint B:(180◦;0,5). Calculate the values ofa(the
amplitude of the graph) andq(the vertical shift of the graph).
30 60 90 120 150 180 210 240 270 300 330 360
2
1
1
2
A
B
x
y
5.On the graph below you see a tangent curve of the following form: y=atan+q. Two points are
labelled on the curve:Point Ais at
(
0 ◦;^13
)
, andPoint Bis at
(
45 ◦;^103
)
.
Calculate, or otherwise determine, the values ofaandq.
15 30 45 60 75 90 105 120 135 150 165 180
5
4
3
2
1
1
2
3
4
5
A
B
x
y
Chapter 6. Functions 201