SHORT LEG:
EXACT
VALUES
OF SIN
PRACTICE
MEDIUM LEG:
LONG LEG:
Find each exact value without using a calculator. Leave your answers in fractional form.
(1) sin(150) ______
(2) sin(225) ______
(3) sin(60) ______
(4) sin(90) ______
(5) sin(315) ______
(6) sin(45) ______
(7) sin(120) ______
(8) sin(300) ______
(9) sin(30) ______
(10) sin(330) ______
(11) sin(0) ______
(12) sin(270) ______
(13) sin(360) ______
(14) sin(135) ______
(15) sin(210) ______
(16) sin(240) ______
PRACTICE
Determine the value(s) of theta that would satisfy each equation.
(17) sin(θ) =—
√3
2
θ=_____ _____
1
(21) sin(θ) =— 2
θ=_____ _____
PRACTICE
(18) sin(θ) =
(19) sin(θ) =1
1
2
θ=_____ _____
(22) sin(θ) =
θ=_____
(23) sin(θ) =0
√3
2
θ=_____ _____
θ=_____ _____
(20) sin(θ) =—
√2
2
θ=_____ _____
(24) sin(θ) =—1
θ=_____
Consider the unit circle pictured at right.
y
(25) Locate the spot at 60°. What is the vertical
distance from that spot down to the x-axis?
________
(26) Prove your answer to
#25 using trigonometry.
x
PROOF:
(27) How can you use similar trigonometric methods
to determine the horizontal distance from the same
spot to the y-axis? Describe/show your method below.
DESCRIPTION / WORK:
(28) Complete the following statement:
If the sin function determines a spot’s vertical
dimensions, then the ______ function
determines a spot’s _______________ dimensions.
WHEN TO USE SIN
PRACTICE
WHEN TO USE COS
Find each exact value without using a calculator. Leave your answers in fractional form.
(29) cos(150) ______
(30) cos(225) ______
(31) cos(60) ______
(32) cos(90) ______
(33) cos(315) ______
(34) cos(45) ______
(35) cos(120) ______
(36) cos(300) ______
(37) cos(30) ______
(38) cos(330) ______
(39) cos(0) ______
(40) cos(270) ______
(41) cos(360) ______
(42) cos(135) ______
(43) cos(210) ______
(44) cos(240) ______
PRACTICE
Determine the value(s) of theta that would satisfy each equation.
(45) cos(θ) =—
√3
2
θ=_____ _____
1
(49) cos(θ) =— 2
θ=_____ _____
PRACTICE
(46) cos(θ) =
(47) cos(θ) =1
1
2
θ=_____ _____
(50) cos(θ) =
(48) cos(θ) =—
θ=_____
θ=_____ _____
(51) cos(θ) =0
√3
2
(52) cos(θ) =—1
θ=_____ _____
θ=_____ _____
√2
2
θ=_____
Use the unit circle to answer each equation.
(53) Which of the following is equivalent to sin(120°)?
a) sin(240°)
b) sin(60°)
c) sin(300°)
d) sin(−120°)
(54) Which of the following is equivalent to cos(210°)?
a) cos(60°)
b) cos(330°)
(55) Which statement is NOT true?
c) cos(120°)
d) cos(−150°)
a) sin(315) ≥ cos(120)
b) cos(300) < sin(60)
c) sin(225) ≤ cos(225)
d) sin(30) ≥ cos(60)
(56) Select all of the following expressions that are equivalent to —1.
a) cos(180)
b) sin(270)
c) cos(−180)
d) cos(90)
e) sin(−90)
f) sin(630)
(57) What is cos(30) + sin(240) ?
a) 0
b) 1
c) √3
d) −√3
REVIEW
(58) If 𝑔(𝑥) = √𝑥 and
ℎ(𝑥) = 𝑥 − 1, what is 𝑔 ℎ(4) ?
REVIEW
b) 7
c) √11
d) √63
Graph each system of inequalities. Shade/darken only the solution region.
(59) 𝑥 ≤ 2
𝑦 < −2𝑥 + 1
REVIEW
a) 5
(60) 𝑥 + 𝑦 < 2
𝑥 > −2
(61) 𝑦 ≥ −2
𝑥<3
(62) 𝑥 + 𝑦 ≥ −2
−5𝑥 + 𝑦 < −3
(65) (66)
Simplify each expression.
(63)
(64)
_______
_______
_______
_______
REVIEW
(67) There are 150 virus cells in a living sample. The virus is reproducing rapidly; the number of virus cells increases by 6% each hour. The sample
will die when it contains 2000 virus cells. How long from now will the sample die? ________
REVIEW
(68) Solve: 9
REVIEW
(69) Solve: 4
= 27
= 32
(70) If (𝑥𝑦 − 5𝑧) is a
factor of the expression 𝑥 𝑦 − 125𝑧 ,
then what else is a factor?
REVIEW
REVIEW
a) 3/8
b) 2/5
c) 6/5
d) 2/3
a) —4
b) 3
c) —2
d) 4
a) (𝑥 𝑦 − 5𝑥𝑦𝑧 + 25𝑧 )
c) (𝑥𝑦 − 5𝑧)(𝑥𝑦 − 5𝑧)
b) (𝑥 𝑦 + 5𝑥𝑦𝑧 + 25𝑧 )
d) (𝑥 𝑦 − 10𝑥𝑦𝑧 + 25𝑧 )
Use long/polynomial division to answer each question.
(71) Using the graph at right, write
the polynomial in factored
form: 𝑦 = 5𝑥 − 14𝑥 − 53𝑥 − 10
y
(72) Factor the polynomial:
𝑥 + 3𝑥 − 9𝑥 − 27
HINT: ONE OF ITS FACTORS IS (𝑥 + 3)
(–2, 0)
y=_____________________________
_____
_______ _______ _______
DEGREE
ROOTS
___________________________