Trigonometric Ratios Worksheet Page 6
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22B
3. The coordinates of a point on the
terminal arm of an angle are
6. The coordinates of a point F on the
given. Determine the exact primary
terminal arm of an angle are shown.
trigonometric ratios for .
y
a) E(−5, 8)
12
b) F(7, −2)
8
F(8, 6)
c) G(−3, −5)
4
d) H(2, 3)
e) I(, −1)
x
0
4
8
12
�12
�8
�4
f ) J(4, −)
�4
g) K(−7, 9)
�8
h) L(5, −3)
�12
4. One of the primary trigonometric
ratios for an angle is given, as well as
a) D etermine the primary trigonometric
the quadrant in which the terminal arm
ratios for angle .
lies. Determine the other two primary
b) D etermine the coordinates of the
trigonometric ratios. Give exact answers.
endpoints of the terminal arm for
a) sin A = 4
__
, quadrant I
each angle.
5
5
__
b) cos B = −
, quadrant III
i) 180° −
8
ii) 180° +
__
c) tan C = −
5 , quadrant II
iii) 30° −
4
__
d) sin D =
, quadrant I
9
c) D etermine the primary trigonometric
e) cos E = 4
___
, quadrant III
ratios for each of the angles in part b).
11
d) H ow do the trigonometric ratios
__
f ) tan F = −
, quadrant IV
5
for angle and the angles in part b)
10
___
compare?
g) tan G = –
, quadrant IV
3
5
__
h) cos H =
, quadrant IV
7. Consider ∠A in quadrant I, such that
9
12
___
.
sin A =
5. Determine the exact primary
13
a) Draw a diagram.
trigonometric ratios for each angle. You
may wish to use a unit circle to help you.
b) D etermine exact values for cos A and
tan A.
a) ∠A = 150°
c) H ow would your answers to parts
b) ∠B = 90°
a) and b) change if the quadrant
c) ∠C = 135°
in which ∠A was located was not
d) ∠D = 300°
specified?
e) ∠E = 330°
f ) ∠F = 240°
8. Suppose ∠B lies in quadrant II and
7
___
. Draw a diagram, and then
g) ∠G = 225°
cos B = −
25
h ) ∠H = 180°
determine exact values for sin B and tan B.
MHR • Chapter 1 978-0-07-090893-2
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