Is $(\sin 48)/2$ the same as $\sin 24$? Does $(\sin 48)/2$ simplify to $\sin 24$? I appreciate the fact the sine graph is curved, so would this mean that you could not simply divide the $48$ on the end to receive the correct answer.
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6No, they are different. – Umberto P. Mar 12 '15 at 16:53
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Possibly related link – najayaz Mar 12 '15 at 16:57
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How would I go about solving 2x=sin48 between a given range? – Toby Cannon Mar 12 '15 at 16:57
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$ x=\sin(48^0)/2$ , thats all. – Narasimham Mar 12 '15 at 17:07
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They're different because $(\sin 48)/2 = \sin 24 \cos 24 \neq \sin 24$.
kobe
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Right thankyou, that's kind of what I thought, but I thought I'd double check, that being said how would I go about solving 2x=sin48 between a given range? – Toby Cannon Mar 12 '15 at 16:58
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@TobyCannon the equation $2x = \sin 48$ is a linear equation in $x$. It's not a trigonometric equation like $\sin^2 x = \cos x$. – kobe Mar 12 '15 at 17:02
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You cannot treat the argument of the sin function as a number you can manipulate with constants outside of the scope of $\sin$.
However, since $\sin(2a) = 2\sin a \cos a$, we have $$\dfrac{\sin(48)}2 = \dfrac{\sin (2(24))}2 = \dfrac{2\sin(24)\cos(24)} 2 = \sin (24)\cos (24)$$
amWhy
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