Trigonometric Ratios Worksheet Page 10
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2211. The point T(3, 4) is on the terminal arm
15. Draw a diagram, and then determine
of ∠B in standard position.
values for the other primary trigonometric
ratios, to four decimal places.
a) Draw and label a diagram.
a) sin A = 0.9138; ∠A lies in
b) Explain how you would determine the
quadrant I
primary trigonometric ratios for ∠B.
b) cos B = −0.2145; ∠B lies in
c) Determine the three primary
quadrant II
trigonometric ratios for ∠B.
c) tan C = −8.144; ∠C lies in
d) Explain how you would determine
quadrant IV
the measure of ∠B.
e) Determine the measure of ∠B to the
16. Determine the approximate measures of
nearest degree.
all angles from 0° to 360° in each case.
° to 360° in each case.
to 360° in each case.
° in each case.
in each case.
f) How would the answer for parts a),
a) The sine ratio is 0.3195.
c), and e) change if point T was
b) The tangent ratio is 1.4385.
reflected in the x-axis?
c) The cosine ratio is −0.7431.
g) How would the answer for parts a),
1
__
17. a) I f cos =
, find two possible values
, find two possible values
c), and e) change if point T was
3
for sin .
reflected in the y-axis?
b) For each value of sin from part a),
find the value(s) of .
12. Consider an angle, ∠C, that lies in
quadrant III, such that tan C = 0.4663.
18. The point S(−5, −6) is on the terminal
a) Draw a diagram to represent this
arm of ∠A.
situation.
a) Determine the primary trigonometric
b) Determine the measure of ∠C to
ratios for ∠A.
the nearest degree. Explain how you
b) Determine the measure of ∠A.
determined the measure of ∠C.
c) Determine the primary trigonometric
ratios for ∠B such that sin B = sin A.
13. Use a calculator to find the values of
d) Determine the measure of ∠B.
to the nearest degree, where
0° ≤ ≤ 360°. °. .
C
a) sin = 0.7312
b) cos = 0.4538
19. a) Solve 2x
2
− x − 1 = 0.
c ) tan = −1.7321 d) sin = 0.9534
b) Explain how the equation in part a)
e ) cos = 0.8862
f ) tan = 1
is related to 2 sin
2
− sin − 1 = 0.
c) Solve 2 sin
2
g) sin = −0.7317 h ) cos = −0.3640
− sin − 1 = 0.
i ) tan = 2.4751
j) sin = −0.9511
20. Determine all the possible measures of ,
k) cos = 0.1829
l) tan = 0.0543
where 0° ° ≤ ≤ 360°. °. .
2
2
a) cos
− 1 = 0
b) tan
= 3
14. Determine another angle that has the
a + b
_____
same trigonometric ratio as each given
21. Given tan A
tan A A =
and ∠A in
a − b
angle. Draw a sketch with both angles
quadrant I, determine expressions for
labelled.
sin A and cos A. State any restrictions on
a) sin 75°
b) cos 190°
the values of a and b.
c) tan 355°
d) sin 252°
10 MHR • Chapter 1 978-0-07-090893-2
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