Everything Maths Grade 10

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