Trigonometry 4 - [Pure 3].

Question 1

What Trig Identity is given in the formula booklet for sin?

Answer 1

sin(A ± B) = sinAcosB ± cosAsinB.

Known as the Addition Formulae.

Question 2

What Trig Identity is given in the formula booklet for cos?

Answer 2

cos(A ± B) = cosAcosB ∓ sinAsinB.

Known as the Addition Formulae.

Question 3

What Trig Identity is given in the formula booklet for tan?

Answer 3

tan(A ± B) = (tanA ± tanB) / (1∓ tanAtanB).

Known as the Addition Formulae.

Question 4

What is the Double Angle Formulae for sin?

HAVE TO REMEMBER - NOT GIVEN IN FORMULA BOOKLET!

Answer 4

sin2A =
* 2(sinAcosA).

Question 5

What are the Double Angle Formulae for cos?

HAVE TO REMEMBER - NOT GIVEN IN FORMULA BOOKLET!

Answer 5

cos2A =
* cos²A - sin²A.
* 2cos²A - 1.
* 1 - 2sin²A.

Question 6

What is the Double Angle Formulae for cos with both sin and cos?

Answer 6

cos2A = cos²A. sin²A.

Question 7

What is the Double Angle Formulae for cos with only cos?

Answer 7

cos2A = 2cos²A - 1.

Question 8

What is the Double Angle Formulae for cos with only sin?

Answer 8

cos2A = 1 - 2sin²A.

Question 9

What is the Double Angle Formulae for tan?

HAVE TO REMEMBER - NOT GIVEN IN FORMULA BOOKLET!

Answer 9

tan2A =
* 2tanA / 1 - tan²A.

Question 10

How do you work out ‘R’ and ‘α’ in the Rsin(θ + α) and Rcos(θ + α) forms?

Answer 10

1. Use the Addition Formulae in formula booklet to expand out sin(θ + α) or cos(θ + α).
2. Make them so you have Rcosα = a and Rsinα = b, where ‘a’ and ‘b’ are integers from the form given.
3. Make a triangle using cosα = a/R and sinα = b/R and use tan to find α.
4. Find the Hypotenuse (R) using Trigonometry.