Name: __________________________________________ Date: _________________________
MCR 3U Quiz (Chapter 5)
Knowledge/U
Thinking/I
/22
Application
/20
Communication
/16
TOTAL
/6
/64
1. a) For each triangle below, calculate csc 𝜃 , sec 𝜃 and cot 𝜃. [K: 10]
b) For each triangle, use one of the reciprocal ratios from part (a) to determine 𝜃 to the nearest degree.
i)
ii)
2. A kite is flying 8.6m above the ground at an angle of elevation of 41 o. Calculate the length of
the string, to the nearest tenth of a meter, needed to fly the kite using [A: 4]
a) a primary trig ratio
b) a reciprocal trig ratio
3. Determine the exact value of each trigonometric expression. [K: 4]
a) sin30o x tan60o – cos30o
b) tan230o – cos245o
4. Determine the exact area of each large triangle. [T: 6]
a) tan𝛼 = 1
b) cos 𝛽 =
√3
2
5. Given each point P(x, y) lying on the terminal arm of angle 𝜃,
i) state the value of 𝜃, using both a counter-clockwise and clockwise rotation. [T: 4]
ii) determine the primary trigonometric ratios. [K: 4]
a) P(-1, -1)
b) P(0, -1)
6. Factor the following expressions. [K: 4]
a) sin2𝜃 – 2sin 𝜃 + 1
b) cos 𝜃 – cos2 𝜃
7. Prove the following identities. [T: 6]
a)
sin2 𝛼
1−cosα
= 1 + cos𝛼
b) tan 𝜃 +
1
𝑡𝑎𝑛𝜃
=
1
sin𝜃cos𝜃
8. Is csc2 𝜃 + sec2 𝜃 = 1 an identity? Prove that it is true or demonstrate why it is false. [C: 4] [T: 4]
9. Alvin’s backyard garden is in the shape of triangle ABC below, BC = 2.0, and D is the midpoint
of BC. Alvin wants to put a fence on the line AB. Determine AB, to the nearest tenth, if Angle
ADB = 45o and Angle ACB = 30o. [A: 4]
10. A coast guard helicopter hovers between an island and a damaged sailboat. [A: 8] [C: 2]




From the island, the angle of elevation to the helicopter is 73o
From the helicopter, the island and the sailboat are 40o apart
A police rescue boat heading towards the sailboat is 800m away from the scene of the
accident. From this position, the angle between the island and the sailboat is 35 o
At the same moment, an observer on the island notices that the sailboat and police
rescue boat are 68o apart.
Explain how you would calculate the straight-line distance, to the nearest meter, from the
helicopter to the sailboat. Justify your reasoning with calculations.
BONUS QUESTIONS
1. What is the next line in the following pattern?
2. Seven matchsticks form two squares as shown in the illustration. Move three matchsticks to
get three squares. You can rotate matchsticks, but you can't overlap and/or damage them.