MCR 3U1 – MS. CONRAD
Unit 5: Trig Ratios
NAME: ____________________
DATE: ____________________
KN:
/15
AP:
/15
CM:
/10
KNOWLEDGE (15 Marks)
1. Fill in the table with the appropriate values. (5 marks)
Question
a) csc  1.425
Answer
b) sec  1.236
c) cot 63o
d) csc 81o
e) sec 124 o
2. Find the EXACT value of each trig ratio. Include a sketch of each angle in
standard position. (6 marks)
a) cos 315o
b) sin 210o
c) tan 1200
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MCR 3U1 – MS. CONRAD
Unit 5: Trig Ratios
3. If 0  A  360 , what are the possible values of A to the nearest degree for
the following? (4 marks)
a) cos A 
1
2
4. Find the EXACT value of
b) tan A  
1
3
tan 30  sin 60 cos 60 . (3 marks)
APPLICATION (15 Marks)
5. Given the point P(-8, -6):
a) Sketch the angle in standard position and determine the exact value of all
SIX trigonometric ratios. (4 marks)
b) Determine the value of the principal angle to the nearest degree. (1 mark)
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MCR 3U1 – MS. CONRAD
Unit 5: Trig Ratios
For questions 6 – 8, you must include a sketch with your solution!!
6. To support a new 2.5-m wall in the construction of a home, the carpenters
nail a piece of wood from the top of the wall to the floor, with the piece of
wood forming the hypotenuse of a right triangle it makes with the wall and
floor. The piece of wood is nailed to the ground such that it makes a 30° angle
with the floor. Determine the EXACT length of the piece of wood. (3 marks)
7. A triangular plot of land is enclosed by a fence. One side of the fence is 200.8
metres long with an opposite angle of
. An adjacent side of the fence is
124.2 metres long with an opposite angle of . Determine to the nearest
tenth of a degree. (3 marks)
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MCR 3U1 – MS. CONRAD
Unit 5: Trig Ratios
8. The posts of a hockey net are 2.0 m apart. A player attempts to score by
shooting the puck along the ice from a point 12.0 m from one post and 10.1
m from the other. Within what angle must the shot be made? Round your
answer to the nearest degree. (4 marks)
COMMUNICATION (10 Marks)
9. Describe how you would find the exact value of cos 210o. You do not need
to solve it, just describe the steps you would take. (3 Marks)
10. EXPLAIN why 0.7071067812 is not the EXACT value of sin 45°. (2 marks)
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MCR 3U1 – MS. CONRAD
Unit 5: Trig Ratios
11. Explain why the sine and cosine of an angle are always less than 1, but the
cosecant and secant of an angle are always greater than 1. (2 Marks)
12. The tan key on your calculator is broken. Describe how you would find
tan 53o. (3 marks)
BONUS QUESTION
The terminal arm of angle  has a slope of -1. If 0    360
a) What are the possible values of sin  ? (3 marks)
b) What are the possible values of  ? (1 mark)
RANDOM QUESTION
What is your favourite Christmas carol/song? ______________________
(1 Bonus Mark if you guess Ms. Conrad’s!)
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