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WorksheetsReview of Trig Identities Unit
Total questions: 30
Worksheet time: 4hrs 18mins
Name
Class
Date
1.
Find Sin (2A) when A = π
a)
109/1000
b)
-1
c)
1
d)
0
2.
Find Cos (2A) when A = π/2
a)
1
b)
0
c)
-1
d)
998/1000
3.
Using the first identity, find Sin(180)
a)
2sin(90)cos(90)
b)
2sin(180)cos(180)
c)
sin(90)cos(90)
d)
sin(180)cos(180)
4.
Using the second identity, find Cos(50)
a)
sin2(25) - cos2(25)
b)
cos2(50) - sin2(50)
c)
cos2(25) - sin2(25)
d)
sin2(50) - cos2(50)
5.
Using the third identity, find Cos(40)
a)
2cos2 (40) - 1
b)
2cos2 (20) - 1
c)
2cos2 (20) + 1
d)
2cos2 (40) + 1
6.
Using the fifth identity, find Tan(200)
a)
2tan(100)/(1-tan2(100))
b)
2tan(200)/(1-tan2(200))
c)
(1-tan2(100))/2tan(100)
d)
(1-tan2(100))/2tan(100)
7.
Which identity does not represent a double-angle identity for cos 2θ?
a)
2sinθcosθ
b)
cos2θ - sin2θ
c)
1 - 2sin2θ
d)
2cos2θ - 1
8.
expand
cos(2θ)
cos(2θ)
a)
cos2θ-sin2θ
b)
2sinθcos
c)
2cos2+1
d)
sin2θ-1
9.
expand
tan(2θ)
tan(2θ)
a)
2cos2θ/1-sin2θ
b)
sin2θ/cos2θ
c)
2tanθ/1-tan2θ
d)
2/cotθ+tanθ
10.
Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ
a)
-1/5
b)
24/25
c)
-24/25
d)
-25/24
11.
Use a double-angle identity to find the exact value of each expression
sin θ = −3/5 and 3π/2 < θ < 2π
Find tan 2θ
sin θ = −3/5 and 3π/2 < θ < 2π
Find tan 2θ
a)
-24/7
b)
24/7
c)
1
d)
-1
-3/4
-3/4
12.
Use a double-angle identity to find the exact value of the following expression.
tan θ= - 2√10/3 and 90<θ<180
Find sin 2θ
tan θ= - 2√10/3 and 90<θ<180
Find sin 2θ
a)
-12√10/49
b)
336/625
c)
336/527
d)
120/119
13.
Use a double-angle identity to find the exact value of the following expression.
cos θ= 15/17 and 3π/2 < θ < 2π
Find cos 2θ
cos θ= 15/17 and 3π/2 < θ < 2π
Find cos 2θ
a)
-240/161
b)
240/161
c)
-240/289
d)
161/289
14.
Which identity represents a double-angle identity for sin 2θ?
a)
2sinθcosθ
b)
cos2θ - sin2θ
c)
1 - 2sin2θ
d)
2cos2θ - 1
15.
Which identity does not represent a double-angle identity for cos 2θ?
a)
2sinθcosθ
b)
cos2θ - sin2θ
c)
1 - 2sin2θ
d)
2cos2θ - 1
16.
Solve the following equation for 0 ≤ x ≤ 2π. sin 2x + sin x = 0
a)
x = 0, 2π/3, π, 4π/3
b)
x = 0, -2π/3, π, 4π/3
c)
x = 0, 2π/3, -π, 4π/3
d)
x = 0, 2π/3, π, -4π/3
17.
Solve the trigonometric equation sin2 2θ = 2sin2θ for θ in the interval [0, π/2)
a)
0 and π/4
b)
0 and π/6
c)
0 and π/2
d)
π/3 and π/6
18.
Solve the following equation for 0 ≤ x ≤ 2π. cos 2x - 1 = sin2x
a)
x = 0, π
b)
x = -1, π
c)
x = 2, π
d)
x = 0, -π
19.
Solve the following equation for 0 ≤ x ≤ 2π. sin 2x cos x = sin x.
a)
x = 0, π/4, 3π/4, π, 5π/4, 7π/4
b)
x = 0, -π/4, 3π/4, π, 5π/4, 7π/4
c)
x = 0, π/4, -3π/4, -π, 5π/4, 7π/4
d)
x = 0, π/4, -3π/4, π, -5π/4, 7π/4
20.
Write the following expression as the sine, cosine, or tangent of an angle.
cos(175)cos(55)+sin(175)sin(55)
cos(175)cos(55)+sin(175)sin(55)
a)
sin(120)
b)
cos(120)
c)
cos(230)
d)
sin(230)
21.
Use Sum or Difference Identities to find the exact value of each expression.
cos(75°)
cos(75°)
a)
1/4
b)
(√6 - √2) / 4
c)
(√6 + √2) / 4
d)
(-√6 - √2) / 4
22.
Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ
a)
-1/5
b)
24/25
c)
-24/25
d)
-25/24
23.
Please select the correct solution
a)
csc x
b)
sec x
c)
cot x
d)
tan x
24.
Please select the correct solution
cos 2 x + sin 2 x=
cos 2 x + sin 2 x=
a)
1
b)
csc 2 x + sec 2 x
c)
sin 2 x
d)
1 - sin 2 x
25.
Simplify.
a)
sin x
b)
cos x
c)
tan x
d)
1
26.
What is the radius of a unit circle?
a)
1
b)
2
c)
1/2
d)
0
27.
What is a complete circle in radians?
a)
π
b)
2π
c)
1/2 π
d)
1
28.
What are the coordinates of 210° on the unit circle?
a)
(−√3/2, −1/2)
b)
(√3/2, −1/2)
c)
(−√3/2, 1/2)
d)
(−1/2,−√3/2 )
29.
4π/3 is equal to how many degrees?
a)
60°
b)
240°
c)
300°
d)
120°
30.
Given sin α = -3/5, cos α = -4/5 and cos β = (2√5)/5, sin β = (-√5)/5
Please find the sum and difference:
sin (α-β)=
Please find the sum and difference:
sin (α-β)=
a)
0
b)
(-10√5)/25
c)
(√2-√6)/4
d)
(√8)/4
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