Name: _________________________
Test Chapter 5 – Trigonometric Ratios
Knowledge
Communication
Application
22
10
41
Clarity of
Thought
Mathematical
Conventions
Part I – Knowledge
Answer each of the following questions in the space provided. Show all of your work.
1. A guy wire supporting a TV antenna forms an angle of 55○ with the ground. The wire is attached to the
antenna 3.71 m above the ground. What is the length of the wire? (3)
2. Find the exact value of the following. (7)
(sin 45)(cos 45) + (sin 30)(sin 60)
3. Find the exact value of sin 225. (3)
1−
sin 45
cos 45
4. For each of the following determine the missing measure. (6)
5. Simplify each expression. (3)
(1 − sin 𝛼)(1 + sin 𝛼)
𝑐𝑜𝑠𝜃 − 𝑐𝑜𝑠 2 𝜃
Part II – Communication
Answer each of the following questions in the space provided. Be sure to use full sentences.
1. What is the purpose of the CAST rule? (2)
2. How does knowing the coordinates of a point P in the Cartesian plane help you determine the trigonometric
ratios associated with the angle formed by the x-axis and a ray drown from the origin to P? (2)
3. When would you use the sine law? What information do you need? What information does it allow you to
find? (3)
4. Explain what the “ambiguous case” means. (3)
Part III – Application
Answer each of the following questions in the space provided. Show all of your work.
1. A 5m stepladder propped against a classroom wall forms an angle of 30○ with the wall. Exactly how far is
the top of the ladder from the floor? Express your answer in radical form. (4)
2. Use each trigonometric ratio to determine all values of θ, to the nearest degree, if 0˚ ≤ 𝜃 ≤ 360˚. (8)
tan 𝜃 = −0.1623
sin 𝜃 = −0.7503
3. Prove each of the following identities. (8)
1
1 + sin ∝
+ tan ∝ =
cos ∝
cos ∝
cos 2 𝑥 = (1 − sin 𝑥)(1 + sin 𝑥)
4. Farmer Goldie McDonald is planning to lay a water pipe through a small hill. She wants to determine the
length of pipe needed. From a point off to the side of the hill on level ground, she runs one rope to the
pipe’s entry point and a second rope to the exit point. The first rope measures 14.5 m, the second measures
11.2 m, and the meet an angle of 58○. What is the length of pipe needed? At what angle with the first rope
should the pipe be laid so that it comes out of the hill at the correct exit point? (7)
5. A lighthouse OT stands on a horizontal plane. O, P and Q are points on the plane. The lighthouse OT is due
north of P. The angle of elevation of a man at P to the lighthouse is 30º. He walks a distance of 500 metres
to point Q. Given that the bearing of Q from P is 50º and the bearing of O from Q is 290º, calculate
(i) OQ and OP
(ii) the height of the lighthouse OT,
(iii) the angle of elevation of T from Q.
(14)