Double Angle Identities

Front

What is the double angle identity for sin(2θ)?

Back

sin(2θ) = 2sin(θ)cos(θ)

Front

What is the double angle identity for cos(2θ)?

Back

cos(2θ) = cos²(θ) - sin²(θ) = 2cos²(θ) - 1 = 1 - 2sin²(θ)

Front

What is the double angle identity for tan(2θ)?

Back

tan(2θ) = 2tan(θ)/(1 - tan²(θ))

Front

Using the first identity, find sin(60).

Back

sin(60) = 2sin(30)cos(30) = 2(1/2)(√3/2) = √3/2

Front

Using the second identity, find cos(50).

Back

cos(50) = cos²(25) - sin²(25)

Front

Using the third identity, find cos(40).

Back

cos(40) = 2cos²(20) - 1

Front

Using the fourth identity, find cos(120).

Back

cos(120) = 1 - 2sin²(60) = 1 - 2(√3/2)² = -1/2

Front

Using the fifth identity, find tan(200).

Back

tan(200) = 2tan(100)/(1 - tan²(100))

Front

Which of the following is not a double angle identity for cos 2θ?

Back

2sinθcosθ is not a double angle identity for cos 2θ.

Front

What is the relationship between sin(2θ) and cos(2θ)?

Back

sin(2θ) = 2sin(θ)cos(θ) and cos(2θ) = cos²(θ) - sin²(θ)