AM-2694

R-formula

A Math · Secondary 4 · Hard · R-formula

Given

y = 5\cos x + 12\sin x

, express

y

in the form

R\cos(x-\alpha)

, where

R>0

and

0^\circ<\alpha<90^\circ

.

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

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