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 θ are related by $$\frac { x } { 2 } = 2 r \sin ^ { 2 } \frac { \theta } { 2 }$$ Write a formula for x in terms of cos θ.
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 θ are related by​ $$\frac { x } { 2 } = 2 r \sin ^ { 2 } \frac { \theta } { 2 }$$ ​ Write a formula for x in terms of cos θ.​  ​
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 θ are related by​ $$\frac { x } { 2 } = 2 r \sin ^ { 2 } \frac { \theta } { 2 }$$ ​ Write a formula for x in terms of cos θ.​  ​
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 x2=2rsin⁡2θ2\frac { x } { 2 } = 2 r \sin ^ { 2 } \frac { \theta } { 2 }2x​=2rsin22θ​

When Two Railroad Tracks Merge,the Overlapping Portions of the Tracks $\frac { x } { 2 } = 2 r \sin ^ { 2 } \frac { \theta } { 2 }$