Solutions To Exercises Functions Worksheet Page 10
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13Solutions to Exercises
35
Exercise 3. Determine the values of the trigonometric functions at the angles with
radian measure
a) 97π b) 15π/2 c) −31π/2 d) 19π/4 e) 9π/3 ,f) 21π/6 g) 14π/3 h) 19π/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
Notes
a) 97π
(−1, 0)
0
−1
0
−
−1
−
97π = 2(48)π + π
15π
3π
b) 15π/2
(0, −1)
−1
0
−
0
−
−1
= 2(3)π +
2
2
−31π
−3π
c) −31π/2
(0, 1)
1
0
−
0
−
1
= −14π +
2
2
√
√
−1
1 √
1 √
−1
19π
3π
d) 19π/4
,
−1
−1
−
2
2
= 2(2)π +
√
√
4
4
2
2
2
2
9π
e) 9π/3
(−1, 0)
0
−1
0
−
−1
−
= 2π + π
3
21π
3π
f) 21π/6
(0, −1)
−1
0
−
0
−
−1
= 2π +
6
2
√
√
√
−1
3
3
−1
−1
2 √
14π
2π
g) 14π/3
,
−
3
−2
= 2(2)π +
√
2
2
2
2
3
3
3
3
√
√
−1
−1
−1
−1
−19π
−3π
h) −19π/4
,
1
1
−
2 −
2
= −4π +
√
√
√
√
4
4
2
2
2
2
Exercise 3
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