- (3 marks) PROVE the trigonometric identity:

sin(θ)

csc(θ)

+

cos(θ)

sec(θ)

= 1

- (3 marks) PROVE the trigonometric identity:

sin2

(θ) sec2

(θ) = sec2

(θ) − 1 - 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 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 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? - (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? - (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. - (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. - (4 marks) Find the volume of the following prism, to the nearest cubic metres.

Figure 1: Figure for question 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 - (4 marks) The point (−20, 21) is on the terminal arm of an angle θ in standard

position. Find sin(θ) and cos(θ).