Double angle formulas for AQA A-level Maths

Double angle formulas

This page covers the following topics:

1. Double angle formula for sine
2. Double angle formula for cosine
3. Double angle formula for tangent
4. Problems with double angle formulas

The sine double angle formula involves trigonometric functions of double angles, i.e sin2A.

Double angle formula for sine

The cosine double angle formula involves trigonometric functions of double angles, i.e cos2A.

Double angle formula for cosine

The tangent double angle formula involves trigonometric functions of double angles, i.e tan2A.

Double angle formula for tangent

The sum of two trigonometric functions can be expressed as a single trigonometric function in the form Rcos(x±α) or Rsin(x±α).

Problems with double angle formulas

1

Give the addition formula for sin(A + B).

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Give the addition formula for sin(A + B).

2

Express cos60° by using the functions of 30°.

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cos(2 × 30º) = cos²(30°) − sin²(30°) = 1/2.

Express cos60° by using the functions of 30°.

3

Rsin(x − α) is a way of expression what general equation?

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Asinx − Bcosx

Rsin(x − α) is a way of expression what general equation?

4

Rearrange the equation cos2A = cos²A − sin²A to give an expression for sin(A).

cos2A = cos²A − sin²A
sin²A = cos²A − cos2A
sinA = √(cos²A − cos2A)

√(cos²A − cos2A)

Rearrange the equation cos2A = cos²A − sin²A to give an expression for sin(A).

5

Express Rcos(x − α) in terms of sine and cosine functions with an argument x and positive coefficients A and B.

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Acosx + Bsinx

Express Rcos(x − α) in terms of sine and cosine functions with an argument x and positive coefficients A and B.

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