1.

Sketch the graphs of the following functions:

1.1

y = 3 cos x − 2 and x ∈ [-180° ; 180°]

1.2

y = 1 − sin x and x ∈ [-90° ; 180°]

1.3

y = cos (2x − 60°) and x ∈ [-180° ; 180°]

1.4

y = sin (x − 30°) and x ∈ [-180° ; 180°]

1.5

y = cos (x + 30°) − 1 and x ∈ [-180° ; 180°]

1.6

y = sin (x + 60°) + 1 and x ∈ [-180° ; 180°]

1.7

y = 3sin 2(x + 30°) and x ∈ [-180° ; 180°]

1.8

y = 2cos 3(x − 30°) and x ∈ [-180° ; 180°]

2.

The figures show the graphs of the trigonometric functions given at each question. Use the information

given in the figure to detemine the values of the unknown variables :

3.1

On the same set of axes draw the graphs of f(x) = sin (x − 30°) and g(x) = cos 2x for − 180° ≤ x ≤ 180°

Give the intercepts with the axes and the coordinates of the turning points. [CAPE November 1991]

3.2

Give the period of f.

3.3

Determine x by calculation if f(x) = g(x).

3.4

If the Y-axis is shifted 60° to the right, give the equation of the graph which was represented by f(x).

4.

In the figure, the graphs of f(x) = a cos (x + b) and g(x) = c + sin dx for − 180° ≤ x ≤ 180°

4.1

Determine the values of a, b, c and d

by using the graphs.

4.2

Calculate the value of f(x) if x = 0°

without using a calculator.

4.3

Determine x by using the graphs if

4.3.1

g(x) = 2

4.3.2

f(x) ≥ g(x) Q(13,5° ; 1,45)

4.4

The Y-axis is translated to pass through

the turning point of f, where f(x) reaches

a maximum. Determine an equation

for f in the form y = . . . with reference to the new set of axes.

5.

In the figure, the graphs of f(x) = a cos (x + b) and g(x) = sin cx for − 90° ≤ x ≤ 90° are given.

5.1

Determine the values of a, b and c.

by using the graphs.

5.2

Use the graphs to answer the following

questions:

5.2.1

Write down the range of f.

5.2.2

For what values of x is f(x) decreasing

as x increases?

5.2.3

If x ∈ [−90° ; 0°], for what

values of x is f(x)**.**g(x) ≥ 0?

5.3

If x ∈ [−90° ; 90°], solve the equation

cos (x − 30°) = sin x and hence

write down the values of x in the interval [−90° ; 90°] for which
g(x) > f(x).

6.

In the figure, the graphs of f(x) = a cos (x + b) and g(x) = c sin dx for − 120° ≤ x ≤ 90° are given.

6.1

Write down the amplitude and period of g.

6.2

Determine the values of a, b, c and d.

6.3

Write down the range of g.

6.4

Write down the value(s) of x < 0° for

which f(x)**.**g(x)≥0

6.5

If the Y-axis is moved to the left so as to

pass through the point of intersection of

the given cosine curve and the X-axis,

which function is now represented by

the curve that initially represented

the given sine function?