PRACTICE
(1) Which of the following angles are coterminal with 30°? Select all that apply.
150°
330°
390°
480°
—30°
PRACTICE
(2) Find one positive
angle that is coterminal with 240°. ________
1110°
1950°
(3) Find one negative angle
that is coterminal with 135°. ________
PROVE IT:
PROVE IT:
PRACTICE
(4) Are 210°
and 930° coterminal?
YES
/
(5) Are 90° and
—810° coterminal?
NO
PROVE IT:
YES
/
NO
PROVE IT:
PRACTICE
(6) Which of the following
angles is not coterminal with 60°?
PRACTICE
—330°
a) 780°
c) —1140°
b) 1500°
d) —660°
PROVE IT:
Determine the exact value of each expression below.
(7) sin(120)=_______
(8) cos(180)=_______
(9) cos(0)=_______
(10) sin(210)=_______
(11) cos(135)=_______
(12) sin(60)=_______
(13) cos(60)=_______
(14) cos(360)=_______
(15) sin(240)=_______
(16) cos(300)=_______
(17) cos(150)=_______
(18) sin(315)=_______
(19) cos(720)=_______
(20) cos(495)=_______
(21) sin(870)=_______
(22) sin(1350)=_______
(23) sin(—135)=_______
(24) cos(—180)=_______
(25) sin(—60)=_______
(26) cos(—450)=_______
PRACTICE
Perform each operation using the exact value of each expression.
(27) sin (150) + cos (60) — cos (270) ________
(28) sin (240) + cos (330) ________
(29) sin (300) + cos (150) —[ cos(0) — sin (90) ] ________
(30) 2 sin(225) — cos(135) ________
PRACTICE
Solve for θ.
(31) sin(θ) =
√2
2
θ=_____ _____
(32) cos(θ) =0
θ=_____ _____
(33) sin(θ) =0
θ=_____ _____
1
(34) cos(θ) =— 2
θ=_____ _____
Consider the unit circle below. State the coordinates of each labeled point on the circle.
PRACTICE
H
A
(35) point A ____________
(36) point B ____________
(37) point C ____________
(38) point D ____________
(39) point E ____________
(40) point F ____________
(41) point G ____________
(42) point H ____________
E
B
C
G
D
F
√
(43) Consider the point
, −
. Which of the following degree measures would yield a
point with the same coordinates? Select all that apply.
PRACTICE
150°
300°
380°
570°
660°
—60°
—300°
—780°
DEFINITION:
REFERENCE
ANGLES
PRACTICE
The reference angle for any angle in standard position
EXAMPLE:
Is the positive acute angle formed by the terminal side of the
225°
Angle and the x axis.
300°
_________
_________
REFERENCE ANGLE
REFERENCE ANGLE
Determine the reference angle for each angle given.
(44) 150° ________
(45) 315° ________
REFERENCE ANGLE
REFERENCE ANGLE
(47) 210° ________
(48) 120° ________
REFERENCE ANGLE
REFERENCE ANGLE
(50) 140° ________
(51) 250° ________
REFERENCE ANGLE
PRACTICE
EXAMPLE:
REFERENCE ANGLE
(46) 135° ________
REFERENCE ANGLE
(49) 330° ________
REFERENCE ANGLE
(52) 345° ________
REFERENCE ANGLE
Consider point A on the unit circle below.
(53) Though point A cannot be represented with special right
triangles, how can its y-coordinate be determined?
y
15°
A
x
B
____________________________________________________
(54) How can its x-coordinate be determined?
____________________________________________________
(55) Calculate the coordinates of point A.
Round answers to the nearest hundredth.
(56) Determine the coordinates of point B. ______________
______________
Solve each equation.
REVIEW
(57) 3|2𝑥 − 3| = 15
(58) 16
x=_____ _____
= 64
(59) √𝑥 + 2 = 𝑥 − 4
x=_____
=2+
(61)
x=_____
x=_____ _____
Simplify each expression.
REVIEW
(61)
REVIEW
÷
(62)
_______
+
(63)
_______
_______
Write an exponential expression to represent each scenario. Then find its value.
(64) Buy a car for $11,330; its value
depreciates by 7% per year for 9 years
__________________
(65) Invest $2450 in an account with 24% annual
interest compounded quarterly for 3 years
________
EXPONENTIAL EXPRESSION
__________________
VALUE
________
EXPONENTIAL EXPRESSION
VALUE
REVIEW
(66) Mrs. Doughmaker sells two varieties of treats at her bakery —
cookies and cupcakes. On a typical day, she uses one pound of flour for each
batch of cookies and two pounds of flour for each batch of cupcakes. If yesterday
she made 500 total treats and used 600 pounds of flour, how many cookies did she make?
Find the roots of each parabola. Then make a table and sketch its graph using five points.
REVIEW
(67) 𝑦 = 𝑥 + 2𝑥 − 8
ROOTS:
________
(
VERTEX:
,0) (
(
,
,0)
)
(68) 𝑦 = −(𝑥 − 3)
ROOT:
(
VERTEX:
,0)
(
,
(69) 𝑦 = 2𝑥 + 4𝑥
ROOTS:
)
(
VERTEX:
,0) (
(
,
(70) 𝑦 = 4𝑥 − 4
,0)
)
ROOTS:
VERTEX:
x
x
x
x
y
y
y
y
REVIEW
(71) Which of the following functions
represents the inverse of 𝑓(𝑥) = 2𝑥 − 1?
a) 𝑓
(𝑥) = − 1
b) 𝑓
c) 𝑓
(𝑥) = −
d) 𝑓
(𝑥) = −2𝑥 − 1
(𝑥) = +
(
,0) (
(
,
,0)
)
(72) Which of the following functions
represents the inverse of 𝑓(𝑥) = 𝑥 − 2?
REVIEW
a) 𝑓
(𝑥) = + 2
b) 𝑓
(𝑥) = 2𝑥 + 2
c) 𝑓
(𝑥) = 2𝑥 + 4
d) 𝑓
(𝑥) = 2𝑥 − 2