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When Two Railroad Tracks Merge, the Overlapping Portions of the Tracks

question 176

Multiple Choice

When two railroad tracks merge, the overlapping portions of the tracks are in the shapes of circular arcs (see figure) .The radius of each arc r (in feet) and the angle $\theta$ are related by
$\frac { x } { 2 } = 2 r \sin ^ { 2 } \frac { \theta } { 2 }$
Write a formula for x in terms of cos $\theta$ .
$When two railroad tracks merge, the overlapping portions of the tracks are in the shapes of circular arcs (see figure) .The radius of each arc r (in feet) and the angle \theta are related by \frac { x } { 2 } = 2 r \sin ^ { 2 } \frac { \theta } { 2 } Write a formula for x in terms of cos \theta . A) x = r \left( 1 - \cos \frac { \theta } { 2 } \right) B) x = r ( 1 - \cos \theta ) C) x = 2 r ( 1 - \cos \theta ) D) x = 2 r ( 1 + \cos \theta ) E) x = 2 r \left( 1 - \cos \frac { \theta } { 2 } \right)$

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