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Double angle formulas for SQA Higher 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(xยฑฮฑ) or Rsin(xยฑฮฑ).

Problems with double angle formulas

1

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

image

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

2

Express cos60ยฐ by using the functions of 30ยฐ.

cos(2 ร— 30ยบ) = cosยฒ(30ยฐ) โˆ’ sinยฒ(30ยฐ) = 1/2.

Express cos60ยฐ by using the functions of 30ยฐ.

3

Rsin(x โˆ’ ฮฑ) is a way of expression what general equation?

Asinx โˆ’ Bcosx

Rsin(x โˆ’ ฮฑ) is a way of expression what general equation?

4

Rearrange the equation cos2A = cosยฒA โˆ’ sinยฒA to give an expression for sin(A).

cos2A = cosยฒA โˆ’ sinยฒA
sinยฒA = cosยฒA โˆ’ cos2A
sinA = โˆš(cosยฒA โˆ’ cos2A)

โˆš(cosยฒA โˆ’ cos2A)

Rearrange the equation cos2A = cosยฒA โˆ’ sinยฒA to give an expression for sin(A).

5

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

Acosx + Bsinx

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

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