Chapter 4 Trigonometric Functions

Trigonometric Functions
7.
8.
a
+ 21 = 35
2 2 2
a
2
= 1225 − 441 = 784
a = 784 = 28
opposite 28 4
sinθ
= = =
hypotenuse 35 5
adjacent 21 3
cosθ
= = =
hypotenuse 35 5
opposite 28 4
tanθ
= = =
adjacent 21 3
hypotenuse 35 5
cscθ
= = =
opposite 28 4
hypotenuse 35 5
secθ
= = =
adjacent 21 3
adjacent 21 3
cotθ
= = =
opposite 28 4
24 + b = 25
2 2 2
b
2
= 625 − 576 = 49
b = 49 = 7
opposite 24
sinθ
= =
hypotenuse 25
adjacent 7
cosθ
= =
hypotenuse 25
opposite 24
tanθ
= =
adjacent 7
hypotenuse 25
cscθ
= =
opposite 24
hypotenuse 25
secθ
= =
adjacent 7
adjacent 7
cotθ
= =
opposite 24
11.
12.
length of hypotenuse
sec 45°=
length of side adjacent to 45°
2
= = 2
1
length of hypotenuse
csc 45°=
length of side opposite 45°
2
= = 2
1
π
13. tan = tan 60 °
3
length of side opposite 60°
=
length of side adjacent to 60°
3
= = 3
1
14.
π length of side adjacent to 60°
cot = cot 60°=
3 length of side opposite 60°
1 1 3 3
= = ⋅ =
3 3 3 3
π π
15. sin − cos = sin 45°− cos 45°
4 4
1 1
= − = 0
2 2
π π
16. tan + csc = tan 45°+ csc30°
4 6
1 2
= + = 1 + 2 = 3
1 1
17. π π π ⎛ 3 ⎞⎛ 2 ⎞
sin cos − tan = −1
3 4 4 ⎜
⎟⎜ 2 ⎟⎜ 2 ⎟
⎝ ⎠⎝ ⎠
9.
length of side adjacent to 30°
cos30°=
length of hypotenuse
3
=
2
6
= − 1
4
6 − 4
=
4
10.
length of side opposite 30°
tan 30°=
length of side adjacent to 30°
18.
π π π 3 3−
3
cos sec − cot = 1− =
3 3 3 3 3
1 1 3 3
= = ⋅ =
3 3 3 3
510
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