Worksheet 10: Trigonometry
Grade 10 Technical Maths
1.
2.
For each of the triangles below, give the sin, cos and tan ratios for each angle that is not a
right angle:
a)
b)
c)
d)
e)
f)
Give the reciprocals for each of the following
a)
sin θ
b)
cos θ
c)
tan θ
d)
sec θ
e)
3.
4.
5.
cot θ
f)
1
cosec θ
3
Given that sin 𝐴 = 2 and cos 𝐵 = − 5, find the following without the use of a calculator:
a)
cot 𝐵
b)
𝑐𝑜𝑠𝑒𝑐 2 𝐴 + sec 2 𝐵
c)
sin2 𝐴 + cos2 𝐵
d)
tan2 𝐴 + 2 sec 𝐵 − 3 𝑐𝑜𝑠𝑒𝑐 2 𝐴
e)
cos2 𝐴 + 𝑐𝑜𝑠𝑒𝑐 2 𝐵
f)
1 − 2 sin 𝐴 . sin 𝐵
Given that 2tan 𝐶 − 3 = 0 and 5sin 𝐷 = 4 , find the following without the use of a calculator:
a)
tan 𝐷 + sin 𝐶
b)
cos2 𝐶 + 𝑐𝑜𝑠𝑒𝑐 2 𝐷
c)
cot 𝐷 − cot 𝐶
d)
3 sin 𝐶 + 4 cos 𝐷
e)
sin2 𝐶 + cos2 𝐶
f)
2 cot 𝐷 + 3 tan 𝐶
Given that 3 cos 𝐸 + 2 = 0 and 13 sin 𝐹 − 5 = 0, find the following without the use of a
calculator:
a)
sin 𝐸 + cos 𝐹
b)
sin2 𝐸 + sin2 𝐹
c)
tan 𝐸 − tan 𝐹
d)
cos 𝐸 + 2 sin 𝐸
e)
sin3 𝐸 − cos3 𝐹
f)
𝑐𝑜𝑠𝑒𝑐 𝐸 − sec 𝐹
6.
What is the value of each angle A – F, in questions 3, 4 and 5?
7.
Use your calculator to find the values of each of the following (remember to make sure that
your calculator is set to degrees):
a)
sin 30°
b)
cos 45°
c)
tan 50°
d)
cot 45°
e)
cot 90°
f)
𝑐𝑜𝑠𝑒𝑐 60°
g)
sec 80°
h)
tan 180°
i)
sin 48°
j)
cos 67° + 𝑐𝑜𝑠𝑒𝑐 67°
k)
sin 108° − tan 100°
l)
tan 92° + cos 92°
m)
cos 160° + 2 sin 80°
n)
tan 34° + sin 45° + cos 56°
o)
sec 30° + 𝑐𝑜𝑠𝑒𝑐 30° + cot 30°
8.
Solve the following equations for 𝑥:
a)
3 sin 𝑥 = 2
b)
4 sin 𝑥 − 3 = 0
c)
5 cos 𝑥 + 4 = 0
d)
𝑥 cos 30° = 2
e)
4 tan 𝑥 + 5 = 0
f)
7 tan 𝑥 = 10
g)
cot 𝑥 − 2 = 0
h)
2 𝑐𝑜𝑠𝑒𝑐 𝑥 + 3 = 0
i)
4 sec 𝑥 − 12 = 0
j)
5 sin 𝑥 − 3 = 2 sin 𝑥
k) *bonus question: 6 cos 𝑥 + sec 𝑥 − 5 = 0
9.
Robohan, the Sharp mascot, is standing 20cm away from a coin on the
ground. With an angle of elevation of 30°, how tall is Robohan?
10.
A ladder is 4m high. The base of the ladder is placed 2.5 away from the wall, so that the top of
the ladder just touches the roof. How high is the roof and what angle of elevation is the ladder
placed at?
11.
A football field is 50m long and 20m wide. If Siphiwe runs from one corner of the field,
diagonally across to the other corner, how far did he run?
12.
A hunter is watching a buck while lying on the ground. The buck is 150m away from the
hunter, and the height from the ground to its eye is 90cm. At what angle should the hunter aim
so that he can hit the buck in the eye?
13.
A party planner wants to hang crime tape across the back of a room in a big X (ie from the top
right corner to the bottom left corner, and from the bottom right corner to the top left corner).
The room is 17m wide and the wall is 3 m high, how much crime tape does the party planner
need?
14.
A signal tower is 3km from our house, we look up at the signal tower with an angle of
elevation of 1°. How tall is the signal tower?
15.
A tree growing in the back garden needs to be cut down. Its shadow is 30m long when the
sun has an angle of depression of 35°. How tall is the tree?