Double Angle Identities
Flashcard
•
Mathematics
•
10th - 12th Grade
•
Hard
Wayground Content
FREE Resource
Student preview
8 questions
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1.
FLASHCARD QUESTION
Front
What is the double angle identity for sine?
Back
sin(2θ) = 2sin(θ)cos(θ)
2.
FLASHCARD QUESTION
Front
What is the double angle identity for cosine?
Back
cos(2θ) = cos²(θ) - sin²(θ) or cos(2θ) = 2cos²(θ) - 1 or cos(2θ) = 1 - 2sin²(θ)
3.
FLASHCARD QUESTION
Front
If sin(θ) = 3/5, what is cos(θ) in the first quadrant?
Back
cos(θ) = 4/5 (using the Pythagorean identity: sin²(θ) + cos²(θ) = 1)
4.
FLASHCARD QUESTION
Front
Calculate sin(2θ) if sin(θ) = 3/5 and θ is in the first quadrant.
Back
sin(2θ) = 2sin(θ)cos(θ) = 2 * (3/5) * (4/5) = 24/25
5.
FLASHCARD QUESTION
Front
If sin(x) = 12/13, what is cos(x) in the first quadrant?
Back
cos(x) = 5/13 (using the Pythagorean identity: sin²(x) + cos²(x) = 1)
6.
FLASHCARD QUESTION
Front
Calculate sin(2x) if sin(x) = 12/13 and x is in the first quadrant.
Back
sin(2x) = 2sin(x)cos(x) = 2 * (12/13) * (5/13) = 120/169
7.
FLASHCARD QUESTION
Front
What is the range of θ for the double angle identities?
Back
0 ≤ θ < 2π
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