AM-2540

R-formula

A Math · Secondary 4 · Hard · R-formula

Express

P = 7 + 5\sin\theta + 12\cos\theta

in the form

P = 7 + R\cos(\theta+\alpha)

, where

R>0

and

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

.

$P = 7 + 13\cos(\theta+\tan^{-1}\tfrac{5}{12})$
$P = 7 + 13\cos(\theta-\tan^{-1}\tfrac{5}{12})$
$P = 7 + 13\sin(\theta+\tan^{-1}\tfrac{5}{12})$
$P = 7 + 13\sin(\theta-\tan^{-1}\tfrac{5}{12})$

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