AM-2665

R-formula

A Math · Secondary 4 · Hard · R-formula

The height

h\,\text{cm}

of a structure is given by

h = 50\cos\theta + 120\sin\theta

. Express

h

in the form

R\sin(\theta + \alpha)

, where

R>0

and

\alpha

is an acute angle in radians.

$130\sin\bigl(\theta + \tan^{-1}(\tfrac{5}{12})\bigr)$
$130\cos\bigl(\theta + \tan^{-1}(\tfrac{5}{12})\bigr)$
$130\sin\bigl(\theta + \tan^{-1}(\tfrac{12}{5})\bigr)$
$130\sin\bigl(\theta - \tan^{-1}(\tfrac{5}{12})\bigr)$

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