A-level Maths · Trigonometry

The R-formula

Write a sin x + b cos x as R sin(x + α) or R cos(x − α): R in exact form, α in degrees.

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Question 1

Express 6sin⁡x−8cos⁡x6\sin x - 8\cos x in the form Rsin⁡(x−α)R\sin(x - \alpha), where R>0R > 0 and 0<α<90∘0 < \alpha < 90^{\circ}. Give R in exact form and give α to 2 decimal places.

Your answer
°

Fill in every box. Give numbers like 4.53 or -0.2, or a fraction such as 7/3. Where an exact answer is asked for, use roots, ln and π with no decimals: for example 2√3 or 3π/4.

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