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) $x = 2 r \left( 1 - \cos \frac { \theta } { 2 } \right)$

Question

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) $x = 2 r \left( 1 - \cos \frac { \theta } { 2 } \right)$

Quizplus · Accepted Answer

The Answer of 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) $x = 2 r \left( 1 - \cos \frac { \theta } { 2 } \right)$

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