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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 Purchase answer to see full attachment

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