Trigonometric Ratios Worksheet Page 2
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22A
7. �se �ec�nolo��
�se �ec�nolo�� Use geometry software to
construct a circle with radius 1 unit. Label
Unless otherwise specified, give all answers
the origin O. Construct and label point B
as exact values.
on the circle in quadrant I. Determine the
coordinates of point B.
1. Determine the sine, cosine, and tangent
ratios for each angle.
a) Construct segment OB. Determine
the length of OB. Find the measure
a) 30°
b) 45°
c) 60°
of ∠AOB.
2. a) C opy and complete the table.
b) Drag B until ∠AOB = 30°. Record
the coordinates of point B, the length
sin
of OB, and the measure of ∠AOB.
Exact
Calculator
c) Reflect B and OB in the x-axis.
0°
Record the coordinates of B′ and the
30°
coordinate distance OB′.
45°
d) Construct segment BB′. Determine
the coordinate distance BB′. What
60°
type of triangle is △OBB′?
90°
e) Construct the midpoint, D, of
b) C ompare the exact values of the
BB′. Then, construct segment OD.
trigonometric ratios to the values
Determine the coordinate distances
from the calculator.
OD and DB.
f) How do the distances OD and DB
3. Repeat question for cos and tan .
compare to the coordinates of B?
4. a) W hat reference angle should be used to
How do the distances OD and DB′
find the primary trigonometric ratios
compare to the coordinates of B′?
for 150°?
�) Drag point B around the unit circle.
b) Determine the primary trigonometric
What do you notice?
ratios for 150°.
B
5. a) D raw a 5° angle in standard position
° angle in standard position
angle in standard position
8. Devan started at point A and walked
on a unit circle.
300 m across a park to a store at point C.
b) What reference angle should be used
Sonal started at point A and walked east
to find the primary trigonometric
to point B and then walked north to the
ratios for 5°?
store at point C.
c) F ind the primary trigonometric
C
ratios for 5°.
6. a) a) D raw a 40° angle in standard position
300 m
on a unit circle.
b) S tate two other angles that have the
30°
same reference angle.
A
B
c) F ind the primary trigonometric
a) Determine the distance AB.
ratios of 40°.
b) Determine the distance BC.
d) S tate the primary trigonometric
ratios for the angles in part b).
MHR • Chapter 1 978-0-07-090893-
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