Double Angle Formula

Question 1

What is the double angle formula for sine?

Answer 1

sin(2θ) = 2sin(θ)cos(θ)

Question 2

What is the double angle formula for cosine?

Answer 2

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

Question 3

True or False: The double angle formula for tangent is tan(2θ) = 2tan(θ)/1 - tan²(θ)

Answer 3

True

Question 4

Fill in the blank: The double angle formula for cosine can also be expressed as cos(2θ) = _____ - sin²(θ).

Answer 4

1

Question 5

Calculate sin(2π) using the double angle formula.

Answer 5

0

Question 6

If sin(θ) = 1/2, what is sin(2θ)?

Answer 6

(Find for θ sin inverse)
sin(2θ) = 2sinθcosθ
=2(1/2)(√3/2)
= √3/2

Question 7

What is cos(2θ) when θ = 45°?

Answer 7

cos(90°) = 0

Question 8

Fill in the blank: The double angle formula for tangent is tan(2θ) = _____ / (1 - tan²θ).

Answer 8

2tan(θ)

Question 9

What is the double angle formula for cosine in terms of cosine only?

Answer 9

cos(2θ) = 2cos²(θ) - 1

Question 10

If cos(θ) = 0, what is cos(2θ)?

Answer 10

-1

Question 11

Evaluate tan(2θ) if tan(θ) = 1.

Answer 11

tan(2θ) = 2/(1 - 1) is undefined.

Question 12

Fill in the blank: The double angle formula for cosine can be expressed as cos(2θ) = _____ - 2sin²(θ).

Answer 12

1

Question 13

Determine sin(2θ) when θ = 30°.

Answer 13

sin(60°) = √3/2

Question 14

What is the value of cos(2θ) when θ = 0°?

Answer 14

1