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1. (3 marks) PROVE the trigonometric identity:

sin(θ)
csc(θ)
+
cos(θ)
sec(θ)
= 1

1. (3 marks) PROVE the trigonometric identity:
sin2
(θ) sec2
(θ) = sec2
(θ) − 1
2. Find the solution of each equation within the interval 0 ≤ θ ≤ 2π
a) (2 marks) −3 cos(θ) + 5 = 4
b) (2 marks) 2 sin(2θ) = 1
3. (3 marks) With the usual notation, 4ABC is such that a = 46 m, b = 74 m and
c = 39 m. Find the measure of ∠B.
4. (4 marks) A ship sees a lighthouse which is found to be 9.8 km distant through
the use of radar. The lighthouse is 3 km from a second lighthouse. The angle between
the line of sight between the two lighthouses is 30◦
. What is the angle between the line
of sight between the ship and the lighthouse 2, when looking from lighthouse 1?
5. (4 marks) A farmer has a triangular field with sides that measure 40 metres (side
AB), 35 metres (side BC) and 38 metres (side CA). What are the measures of the angles
A, B and C in this field?
6. (4 marks) In 4RST, RS = 4.9 m, ST = 3.7 m, and RT = 8.1 m. Find the
1
area of 4RST, to the nearest tenth of a square metre.
7. (4 marks) 4P QR has vertices P(1, 5), Q(6, −7), and R(−2, 1). Find the angle
measures, to the nearest tenth of a degree.
8. (4 marks) Find the volume of the following prism, to the nearest cubic metres.
Figure 1: Figure for question 9
9. (10 marks) Determine the length of the chord PQ in each circle, to the nearest
tenth of a meter. a)
Figure 2: Figure for question 10
10. (4 marks) The point (−20, 21) is on the terminal arm of an angle θ in standard
position. Find sin(θ) and cos(θ). 