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AQA June 2009 C4 Question (trig)

Hi,
I am slightly stuck on this question from a June 2009 paper

Express 7sin(x) + 3cos(x) in the form Rsin(x+a), where R >0 and a is an
acute angle. Give your value of a to the nearest 0.1 degrees.

I have got R as √58 but now have no idea how to calculate a.

Thanks

Reply 1

gdunne42

Original post by minibren

One method
Rsin(x + a) = Rsinxcosa+ Rcosxsina
Now compare coefficients in the original question with those from the addition formula above
Rsina = 3 and Rcosa = 7
From there you can find tana and therefore a

Posted from TSR Mobile

(edited 10 years ago)