GRADE 12 TRIGONOMETRY WORKSHEET
Question 1
1.1
If
calculator.
and
, determine the value of
1.2
Calculate, using sketches, the value of
[
if
and
, while
]
without the use of a
in terms of a and b
.
Question 2
2.1
Simplify the following:
2.2
Simplify without a calculator:
2.3
If
a.
, determine:
(
)
b.
c.
d.
Question 3
3.1
Given:
a.
Sketch f and g on the same set of axes for the interval [
b.
Write down the period of f.
c.
Use your graph and write down the value(s) of x for which
]
is a maximum.
3.2
The given curve is that of the function ( )
Y
(
) for
[
]
Y1
(20°;2)
2
C
1
0
110°
B
360°
X
X1
-1
-2
A
The curve of f has turning points at (20°;2) and A. Hence answer the following questions:
a.
Determine the values of a and b.
b.
Write down the x-coordinates of points A and B.
c.
Calculate the y-coordinate of point C. (round off to 1 decimal digit)
d.
The y-axis is translated to the Y1 position and the x-axis to the X1 position.
If f in relation to the new set of axes defines a sine graph, write down a possible
equation of this graph.
Question 4
4.1
a.
Solve for x correct to one decimal place, in the interval [0°;180°]:
(
)
b.
4.2
Find the general solution of the following:
(
)
(
)
Question 5
5.1
Prove the following:
5.1.1
5.1.2
5.1.3
5.2
Expand
in terms of
.
5.3
Find the general solution and solve for θ
[-180;360] in the following:
5.3.1
5.3.2
5.3.3
(
)
(
)
5.3.4
QUESTION 6
Shown below is a netball game with the players about to score. The Netball post is 3.05 metres long, player
1 is 1.62 meters tall and player 2 is 1.7 meters tall. The two players are 3 meters apart and the angle
at the post inbetween them is 135°. If Player 2 is 1 quarter of the way further from the pole than Player 1 the
angle of elevation at which each of them has to throw the ball to score.
1.62