Exam Flashcards
(55 cards)
What is the double angle formula for sine?
sin(2θ) = 2sin(θ)cos(θ)
What is the double angle formula for cosine?
cos(2θ) = cos²(θ) - sin²(θ)
What is an alternate form of the double angle formula for cosine?
cos(2θ) = 2cos²(θ) - 1
What is the formula for tangent of double angle?
tan(2θ) = 2tan(θ) / (1 - tan²(θ))
True or False: The double angle formulas can be derived from the sum formulas.
True
Fill in the blank: The double angle formula for sine can be expressed as _____ .
sin(2θ) = 2sin(θ)cos(θ)
What is the auxiliary angle method used for?
It is used to simplify expressions involving trigonometric functions.
How can you express cos(2θ) using only sine?
cos(2θ) = 1 - 2sin²(θ)
What is the value of sin(90 degrees)?
1
If sin(θ) = 1/2, what is sin(2θ)?
sin(2θ) = 2(1/2)cos(θ) = cos(θ)
True or False: The auxiliary angle helps in solving integration problems.
True
What is the derivative of sin(x)?
cos(x)
What is the integral of cos(x)?
sin(x) + C
What is the formula for the derivative of tan(x)?
sec²(x)
Fill in the blank: The double angle formula for tangent can be expressed as _____ .
tan(2θ) = 2tan(θ) / (1 - tan²(θ))
What is the relationship between sine and cosine in the unit circle?
sin(θ) = y-coordinate, cos(θ) = x-coordinate
What is the double angle formula for sine when θ = 30 degrees?
sin(60 degrees) = 2(1/2)(√3/2) = √3/2
True or False: The double angle formulas are only applicable to acute angles.
False
What is the period of the sine function?
2π
What is the period of the cosine function?
2π
Fill in the blank: The auxiliary angle method often involves converting _____ into a single trigonometric function.
a linear combination of sine and cosine
What is the value of cos(0 degrees)?
1
If cos(θ) = 0, what is θ?
θ = 90 degrees + n*180 degrees, where n is an integer
What is the derivative of cos(x)?
-sin(x)
