# a. Express 1.5 sin 2x + 2 cos 2x in the form R sin (2x + ), where R >

## Question:

a. Express 1.5 sin 2x + 2 cos 2x in the form R sin (2x + α), where R > 0 and 0 < α < π/2 , giving your values of R and α to 3 decimal places where appropriate.

b. Express 3 sin x cos x + 4 cos^{2} x in the form a sin 2x + b cos 2x + c, where a, b and c are constants to be found.

c. Hence, using your answer to part a, deduce the maximum value of 3 sin x cos x + 4 cos^{2} x.

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**Related Book For**

## Pearson Edexcel A Level Mathematics Pure Mathematics Year 2

**ISBN:** 9781292183404

1st Edition

**Authors:** Greg Attwood, Jack Barraclough, Ian Bettison, David Goldberg, Alistair Macpherson, Joe Petran

**Question Details**

Chapter #

**7**Section: Mixed exercise

Problem: 18

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