What is the double angle formula for sine?

Trigonometric Equations and Identities

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Mathematics
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9th - 12th Grade
•
Hard

Ethan Morris
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
sin(2θ) = 1 - 2sin²θ
sin(2θ) = 2sinθcosθ
sin(2θ) = sin²θ - cos²θ
sin(2θ) = 2cos²θ - 1
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in solving the equation sin(2x) + sin(x) = 0?
Add sin(x) to both sides
Use the identity sin(2x) = 2sin(x)cos(x)
Divide both sides by sin(x)
Subtract sin(x) from both sides
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
After factoring out sin(x), what is the resulting equation?
2cos(x) + 1 = 0
2sin(x)cos(x) = 0
sin(x)(2cos(x) + 1) = 0
sin(x) + cos(x) = 0
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Where is sin(x) equal to zero on the unit circle?
π/4 and 3π/4
0 and π
π/3 and 2π/3
π/2 and 3π/2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the cosine double angle formula that involves only cosine?
cos(2θ) = cos²θ - sin²θ
cos(2θ) = 2cos²θ - 1
cos(2θ) = 1 - 2sin²θ
cos(2θ) = 2sinθcosθ
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in solving the equation cos(2x) = cos(x) + 2?
Use the identity cos(2x) = 2cos²(x) - 1
Divide both sides by 2
Subtract cos(x) from both sides
Add 1 to both sides
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of factoring the equation 2cos²(x) - cos(x) - 3 = 0?
(2cos(x) - 3)(cos(x) + 1) = 0
(cos(x) - 3)(2cos(x) + 1) = 0
(2cos(x) + 3)(cos(x) - 1) = 0
(cos(x) + 3)(2cos(x) - 1) = 0
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