Trigonometric Ratios Worksheet Page 7
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9. Given tan C =
with ∠C in quadrant III,
4
a) Use geometry software to construct a
determine exact values for sin C and cos C.
circle with radius 3 units. Plot a point
A on the circle in quadrant I.
10. Consider ∠A in standard position on
9
___
a coordinate grid such that sin A =
b) M easure the distance between point A
41
9
___
and tan A = –
.
and the origin, O. Construct segment
40
OA and label it r. Determine the
a) C an the ratios for sin A and
coordinates of point A.
tan A be used to determine the
y
y
x
quadrant in which ∠A is located?
__
__
__
r ,
r , and
x .
c) Calculate the ratios
Explain.
d) Measure ∠A.
b) Determine the exact value for cos A.
e) C alculate sin A, cos A, and tan A.
c) H ow would your answers for parts a)
Compare your answers to the ratios
and b) change if the ratios were
9
9
from part c).
___
___
?
sin A = –
and tan A =
41
40
d) H ow would your answers for parts a)
C
and b) change if the ratios were
15. An angle is in standard position on a
9
9
___
___
?
sin A = –
and tan A = –
coordinate grid. The terminal arm of
41
40
is in quadrant III on the line defined by
the given equation. Determine the exact
11. Suppose ∠D lies in quadrant IV and
5
____
values of the three primary trigonometric
___
sin D =–
. Determine the exact
√
34
ratios for angle .
values for cos D and tan D.
a) y = x
12. Determine one other angle that has the
b) y = 2x
same trigonometric ratio as each given
angle.
c) y = 4x
a) sin 45°
16. Refer to your answer to question 15. How
b) cos 300°
does tan relate to the equation of the
c) tan 225°
line through the terminal arm?
d) sin 230°
17. A 10-m guy wire is attached to a post at
e) cos 115°
ground level and to the top of a nearby
f ) tan 310°
vertical antenna. The angle formed
between the guy wire and the ground
13. Are the angles in each pair related?
is 60°.
Explain.
a) Determine the height of the antenna
a) 135° and 315°
to the nearest tenth of a metre.
b) 40° and 320°
b) D etermine the horizontal distance
c) 45° and 215°
from the post to the antenna to the
nearest tenth of a metre.
d) 150° and 210°
e) 210° and 330°
f ) 125° and 245°
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