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OCR AS Mathematics Trigonometry
Topic assessment
1. (a) The diagram shows the graph y = sin x and a line parallel to the x-axis.
Given that one point of intersection is when x = 136 , write down the values of A, B
and C.
[3]
(b) The diagram shows the graph y = cos 2 x and a line parallel to the x-axis.
Given that one point of intersection is when x = 24 , write down the values of P and
Q.
[3]
2. In this question you must show detailed reasoning.
 is an obtuse angle and sin  = 0.6 . Work out the exact values of cos  and tan  . [4]
3. You are given that the equation sin  = 0.53, 0    360 has solution  = 32 ,148 .
Write down all the values of x in the range 0  x  360
(a) satisfying the equation sin ( x + 20 ) = 0.53
[1]
x
= 0.53
3
(c) satisfying the equation sin ( 2 x − 10 ) = 0.53
(b) satisfying the equation sin
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[1]
[3]
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OCR AS Maths Trigonometry Assessment
4. Yahya is attempting to prove the cosine rule for the triangle shown below. He starts by
adding the dotted lines as shown.
Here are the first few lines of his proof.
2
y 2 = c2 − (b + x )
[Pythagoras's Theorem]
y 2 = a2 − x2
[Pythagoras's Theorem]
c − b − 2bx = a
[Equating expressions for y 2 and tidying up]
Complete his proof explaining clearly what you have done.
2
2
2
[4]
5. Find the perimeter and area of the triangle shown below.
B
52°
12 cm
A
15 cm
C
[7]
6. Marisa is on a Ferris wheel, watched by her
friend Tash who is directly below the wheel as
shown in the diagram. Tash looks up and sees
Marisa’s capsule directly overhead in position
M1. Exactly 150 seconds later Marisa’s
capsule is directly overhead again in position
M2. The Ferris wheel turns anticlockwise as
shown by the arrow.
Given that the Ferris wheel has radius 15m and
is going at a constant speed and that Tash is a
horizontal distance of 9 m from the lowest
point of the wheel, work out how long the
Ferris wheel takes to make one full revolution.
[6]
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OCR AS Maths Trigonometry Assessment
7. In this question you must show detailed reasoning.
Solve these equations for 0    360 .
3
(a) cos2  =
4
(b) 2sin  cos + sin  = 0
3 sin 3 = cos 3
(c)
[3]
[3]
[3]
8. In this question you must show detailed reasoning.
The diagram shows parts of the curves y = 6sin 2 x and y = 4 + cos x where x is in
degrees.
Solve the inequality 6sin 2 x  4 + cos x for 0  x  360 .
[9]
Total 50 marks
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