Chapter 4 Trigonometric Functions

Trigonometric Functions
3.
π ⎛ 1 1 ⎞
t = , P⎜ , ⎟
4 ⎝ 2 2 ⎠
π 1
csc = =
4 y
2
π 1
sec = =
4 x
2
π x
cot = =
4 y
= 1
1
y
1
2
⎛ π ⎞ ⎛π
⎞
4. a. sec⎜− = sec = 2
4
⎟ ⎜
4
⎟
⎝ ⎠ ⎝ ⎠
5.
b.
⎛ π ⎞ ⎛π
⎞ 2
sin ⎜− sin
4
⎟ =− ⎜ =−
4
⎟
⎝ ⎠ ⎝ ⎠ 2
2
sinθ
tanθ
= =
3
cosθ
5
3
2 3 2
= ⋅ =
3 5 5
2 5 2 5
= ⋅ =
5 5 5
1 1 3
cscθ
= = =
sinθ
2 2
3
1 1 3
secθ
= = =
cosθ
5 5
3
3 5 3 5
= ⋅ =
5 5 5
1 1 5
cotθ
= = =
tanθ
2 2
5
6.
7. a.
1 π
sin t = , 0 ≤ t <
2 2
2 2
sin t+ cos t = 1
2
⎛1
⎞ +
2 =
⎜ cos 1
2
⎟ t
⎝ ⎠
2 1
cos t = 1−
4
3 3
cost
= =
4 2
π
Because 0 ≤ t < , cos t is positive.
2
b.
5π ⎛π ⎞ π
cot = cot π cot 1
4
⎜ + = =
4
⎟
⎝ ⎠ 4
⎛ 9π
⎞ ⎛ 9π
⎞
cos ⎜− cos 4π
4
⎟= ⎜− +
4
⎟
⎝ ⎠ ⎝ ⎠
7π
= cos 4
=
π
8. a. sin ≈ 0.7071
4
2
2
b. csc 1.5 ≈ 1.0025
Exercise Set 4.2
1. The point P on the unit circle has coordinates
⎛ 15 8 ⎞
⎜−
,
17 17
⎟
⎝ ⎠ . Use 15 8
x =− and y = to find the
17 17
values of the trigonometric functions.
8
sin t = y =
17
15
cost
= x = −
17
8
y 17 8
tan t = = = −
15
x − 15
17
1 17
csct
= =
y 8
1 17
sect
= = −
x 15
x 15
cot t = = −
y 8
498
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