Solutions To Exercises Functions Worksheet Page 9
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13Solutions to Exercises
34
Exercise 2. Determine the values of the trigonometric functions at the angles with
radian measure
a) −4π b) 5π/2 c) −7π/2 d) −9π/4 e) 5π/3 f) −11π/6 g) −4π/3 h) 9π/4.
Solution: The following table is derived using the values in
Table
2.2, the symmetry
properties of the unit circle, and the periodic behavior of the trigonometric functions.
t
P
sin
cos
tan
cot
sec
csc
a) −4π
(1, 0)
0
1
0
−
1
−
b) 5π/2
(0, 1)
1
0
−
0
−
1
c) −7π/2
(0, 1)
1
0
−
0
−
1
√
√
1 √
−1
−1
1 √
d) −9π/4
,
−1
−1
2 −
2
√
√
Exercise 2
2
2
2
2
√
√
√
1
−
3
−
3
1
−1
−2
e) 5π/3
,
−
3
2
√
√
2
2
2
2
3
3
√
√
√
3
1
1
3
1 √
2 √
f) −11π/6
,
3
2
2
2
2
2
3
3
√
√
√
−1
3
3
−1
−1
2 √
g) −4π/3
,
−
3
−2
√
2
2
2
2
3
3
√
√
1 √
1 √
1 √
1 √
h) 9π/4
,
1
1
2
2
2
2
2
2
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