AM-2485

R-formula

A Math · Secondary 4 · Hard · R-formula

Express

P=12+5\sin\theta+12\cos\theta

in the form

12+R\sin(\theta+\alpha)

, where

R>0

and

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

.

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

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