AM-991

R-formula

A Math · Secondary 3 · Hard · R-formula

Express

5\sin x+12\cos x

in the form

R\sin(x+\alpha)

, where

R>0

and

0<\alpha<\tfrac{\pi}{2}

.

$13\sin\bigl(x+\tan^{-1}\tfrac{12}{5}\bigr)$
$13\sin\bigl(x-\tan^{-1}\tfrac{12}{5}\bigr)$
$13\cos\bigl(x+\tan^{-1}\tfrac{12}{5}\bigr)$
$13\cos\bigl(x-\tan^{-1}\tfrac{12}{5}\bigr)$

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