# Show that $2θ + 2\sinθ - 1 = \pi/3.$

Need help with this question:

The diagram shows that the cross section ABCD of a glass prism. AD = BC = 4cm and both are at right angles to DC. AB is the arc of a circle, centre O and radius 6cm. Given that angle AOB = 2 radians and that the perimeter of the cross-section is 2(7 + pi), show that (2θ + 2sinθ - 1) = pi/3.

Here is a (bad) diagram of the thing:

What I did so far: I worked out AB arc length = 12θ and I was going to use the cosine rule to work out the direct straight length of AB to find out what CD was, but I don't see how the sin comes into play.

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Hint: Why does the result involve $\sin \theta$ instead of $\sin (2\theta)$? –  hwhm Oct 24 '12 at 19:00

## 1 Answer

Hint: $\frac{DC}2 = 6\sin\theta$.

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