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A Level Stage 1 Prep

Trigonometry

1.

In triangle ABC, AB = 20cm and angle B = 45Ã‚Â°.

(a)

Given that AC = 16 cm, find the two possible values for angle C, correct to 1 decimal place.

[4]

(b)

Given instead that the area of the triangle is 7572 cm, find BC.

[2]

2.

B

8 cm

65Ã‚Â°

30Ã‚Â°

10 cm

The diagram shows triangle ABC, with AB = 8cm, angle BAC = 65Ã‚Â° and angle BCA = 30Ã‚Â°. The point Dis

on AC such that AD = 10cm.

(i)

Find the area of triangle ABD.

[2]

(ii)

Find the length of BD.

[2]

Find the length of BC.

[2]

3.

Ã‘Â

(x + 2)cm

27 cm

60Ã‚Â°

B

x cm

The diagram shows triangle ABC, with AB = x cm, AC = x + 2 cm, and angle CAB = 60Ã‚Â°.

(a)

Find the value of x.

[4]

(b)

Find the area of triangle ABC, giving your answer in an exact form as simply as possible.

[2]

1.05 Trigonometry

A Level Stage 1 Prep

4.

The points P, Q and R have coordinates (-1,6), (2, 10) and (11, 1) respectively. Find the angle PRQ. [4]

5.

Solve each of the following equations, for 0Ã‚Â° SXS 360Ã‚Â°.

(0)

sinx = 0.8

[3]

(ii)

sin x = 3 cos x

[3]

6.

(a)

Show that the equation

2 sin x tan x = cos x + 5

can be expressed in the form

3cos2x + 5 cos x – 2 = 0.

[3]

(b)

Hence solve the equation

2 sin 20 tan 20 = cos 20 +5,

giving all values of 0 between 0 and 180Ã‚Â°, correct to 1 decimal place.

(5)

7

(a)

Solve the equation sinÃ‚Â²x = 0.25 for 0Ã‚Â° S x < 360Ã‚Â°.
[3]
(b)
In this question you must show detailed reasoning.
Solve the equation tan 34 = 73 for 0Ã‚Â° 5Ã‚Â° < 90Ã‚Â°.
[3]
8.
In this question you must show detailed reasoning.
Solve the equation 2cos x = 2-sin x for 0Ã‚Â° S XS 180Ã‚Â°
[5]
1.05 Trigonometry
A Level Stage 1 Prep
9.
Each of the curves shown below is a transformation of part of the curve y = sin x.
Write the equation of each curve.
y
(a)
2
1
0
90Ã‚Â° 180Ã‚Â° 270Ã‚Â° 360Ã‚Â° x
-1
- 2
1
0
90Ã‚Â°
180Ã‚Â° 270Ã‚Â° 360Ã‚Â°
-1
Ã¢ËœÂº
-2
YE
1
(c)
1
90Ã‚Â°
180Ã‚Â° 270Ã‚Â° 360Ã‚Â°
X
-1
-2
y =
[3]
1.05 Trigonometry
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