AM-917

R-formula

A Math · Secondary 3 · Hard · R-formula

A warehouse roof is modelled by

h = 18\sin\theta - 10\cos\theta

, where

h

metres is the height of the entrance and

0^\circ \le \theta \le 90^\circ

. Express

h

in the form

R\sin(\theta - \alpha)

, where

R>0

and

0^\circ \le \alpha \le 90^\circ

.

$2\sqrt{106}\,\sin\bigl(\theta-\tan^{-1}\tfrac{5}{9}\bigr)$
$2\sqrt{106}\,\sin\bigl(\theta+\tan^{-1}\tfrac{5}{9}\bigr)$
$\sqrt{424}\,\sin\bigl(\theta-\tan^{-1}\tfrac{9}{5}\bigr)$
$\sqrt{424}\,\sin\bigl(\theta+\tan^{-1}\tfrac{9}{5}\bigr)$

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