Part II: The Answers
166
Answers
101–200
Because θ is in the second quadrant, you have sinθ = 8
89
and cosθ = − 5
89
. Enter
these values in the identity sin( )
sin cos
2
2
θ
θ
θ
=
and solve:
sin( )
sin cos
2
2
2 8
89
5
89
80
89
θ
θ
θ
=
=

 

  −

 

 
= −
108.
77
85
To find the value of cos( )
2θ , you can use the identity cos( )
s in
2
1 2
2
θ
θ
= −
. Using
cot
,
θ = − 9
2
you can make a right triangle and find the missing side using the
Pythagorean theorem. When making the triangle, you can neglect the negative sign:
h =
+
=
9 2
85
2
2
Now use the identity cos( )
s in
2
1 2
2
θ
θ
= −
. The sine is negative, so you have
sinθ = − 2
85
:
cos( )
s in
2
1 2
1 2
2
85
1 8
85
77
85
2
2
θ
θ
= −
= − −

 

 
= −
=
109.
3
4
π rad
Because 180° = π rad, you have 1 180
° = π rad, so multiply the number of degrees by this
value:
135 135 180
3
4
° =
( ) =
π
π
rad
rad
110.
− 14
9
π rad
Because 180° = π rad, you have 1 180
° = π rad, so multiply the number of degrees by this
value:
−
°= −
( ) = −
280
280 180
14
9
π
π
rad
rad