Part II: The Answers
164
Answers
101–200
103.
sinθ = 7 65
65
; cosθ = 4 65
65
; tanθ = 7
4
When considering the sides of the right triangle, the values of the trigonometric
functions are given by sinθ =
opposite
hypotenuse
, cosθ =
adjacent
hypotenuse
, and
tanθ =
opposite
adjacent
; therefore, sinθ =
=
7
65
7 65
65
, cosθ =
=
4
65
4 65
65
, and
tanθ = 7
4
.
104.
sinθ = 4 17
17
; cosθ = 17
17
; tanθ = 4
When considering the sides of the right triangle, the values of the trigonometric
functions are given by sinθ =
opposite
hypotenuse
, cosθ =
adjacent
hypotenuse
, and
tanθ =
opposite
adjacent
; therefore, sinθ =
=
8
2 17
4 17
17
, cosθ =
=
2
2 17
17
17
, and
tanθ = =
8
2
4.
105.
−2 10
3
You know the value of sinθ , so if you can find the value of cosθ , you can evaluate cotθ
using cot
cos
sin
θ
θ
θ
=
. To find cosθ , use the identity sin
cos
2
2
1
θ
θ
+
= :
3
7
1
1 9
49
40
49
2
2
2
2
( ) + =
= −
=
cos
cos
cos
θ
θ
θ
Next, take the square root of both sides, keeping the negative solution for cosine
because π θ π
2
< < :
cos
cos
cos
2
40
49
40
49
2 10
7
θ
θ
θ
=
= −
= −
Therefore, using cot
cos
sin
θ
θ
θ
=
, you have
cotθ =
−
= −
2 10
7
3
7
2 10
3