(1) From memory, fill in the degree and radian measures on each unit circle.
PRACTICE
DEGREES
RADIANS
Find each exact value without using a calculator.
PRACTICE
(4) sin
2π
3
______
(2) cos(225) ______
(3) sin(150) ______
(6) sin(315) ______
(7) sin
(10) cos(180) ______
(11) sin
7π
4
______
(12) cos
5π
3
(15) cos
π
6
______
(16) cos
π
2
(19) cos
7π
2
(14) sin
π
3
______
(18) sin(600) ______
PRACTICE
7π
6
______
______
(8) cos(330) ______
______
______
(20) sin(6π) ______
(5) cos
3π
4
______
(9) sin
3π
2
______
(13) sin(225) ______
(17) cos(2π) ______
(21) cos −
13π
4
______
Solve for θ such that 0 ≤ θ < 360 and 0 ≤ 𝜃 < 2𝜋.
(22) cos(θ) =
√3
2
θ=__________
DEGREES
=__________
RADIANS
(26) sin(θ) =
√2
2
θ=__________
DEGREES
=__________
RADIANS
1
(23) sin(θ) =— 2
θ=__________
DEGREES
=__________
RADIANS
(27) sin(θ) =0
θ=__________
DEGREES
=__________
RADIANS
(24) cos(θ) =0
θ=__________
DEGREES
=__________
RADIANS
(28) sin(θ) =—1
θ=__________
DEGREES
=__________
RADIANS
(25) cos(θ) =
√2
2
θ=__________
DEGREES
=__________
RADIANS
1
(29) cos(θ) =— 2
θ=__________
DEGREES
=__________
RADIANS
PRACTICE
Determine the value of each expression.
(30) [sin(30°)] + [cos(30°)]
(32) [cos(4𝜋)] + [sin(4𝜋)]
__________
__________
(31) sin
+ cos
(33) [sin 𝜃] + [cos 𝜃]
__________
__________
PRACTICE
(34) Select a point on the unit circle below. State the coordinates of the point you
selected. Then use the coordinates to verify that sin 𝜃 + cos 𝜃 = 1.
ANGLE
SELECTED: ___________
VERIFICATION:
COORDINATES: __________________
PRACTICE
(35) Using the triangle provided, prove that sin 𝜃 + cos 𝜃 = 1.
c
a
Θ
b
VARIATIONS ON THE
PYTHAGOREAN IDENTITY
sin 𝜃 =
cos 𝜃 =
PRACTICE
(36) Use the Pythagorean identity to prove that (sin 𝜃 + cos 𝜃) = 2 sin 𝜃 cos 𝜃 + 1.
PRACTICE
(37) Use a variation of the Pythagorean identity to prove that sin 𝜃 − sin 𝜃 cos 𝜃 = sin 𝜃.
REVIEW
(38)
π
3
REVIEW
Convert the following radians to degrees.
= ______°
(39)
3π
4
= ______°
(40)
5π
3
(41) 2π = ______°
= ______°
Convert the following degrees to radians.
(42) 225°=______
(43) 300°=______
(44) 90°=______
(45) 150°=______
REVIEW
Consider each expression. Write the letter of each expression in the blanks to satisfy the
inequality statement provided at right.
(46)
A
B
C
D
E
cos(180)
sin(360)
cos(120)
cos(330)
sin(45)
A
B
C
D
E
sin(90)
cos(135)
cos(210)
sin(30)
sin(120)
(47)
REVIEW
√
(52) Which value is equivalent to cos(
4π
3
5π
3
b) cos( )
√
, −
√
(51)
2π
)
3
−
√
,
Θ=_______
?
π
3
c) cos( )
d) sin(
11π
)
6
π
(53) Which value is not equivalent to sin( 4 ) ?
π
4
3π
4
a) cos( )
REVIEW
−
Θ=_______
Θ=_______
a) sin( )
REVIEW
(50)
(49) (0 , −1)
Θ=_______
REVIEW
_____ < _____ < _____ < _____ < _____
Consider each point on the unit circle. Determine the value of each angle.
− ,
(48)
_____ < _____ < _____ < _____ < _____
b) sin( )
c) cos(315)
d) sin(225)
Use special right triangles to find the lengths of the missing sides.
(54) x=_______
y=_______
22
y
30°
x
(55) x=_______
y
y=_______
60° x
(56) x=_______
y=_______
16√3
y
x
45°
6