Use the figure below to determine the exact value of the given function. $\sin 2 \theta$

A) $\sin 2 \theta = \frac { 5 } { 13 }$
B) $\sin 2 \theta = \frac { 7 } { 13 }$
C) $\sin 2 \theta = \frac { 12 } { 5 }$
D) $\sin 2 \theta = \frac { 9 } { 13 }$
E) $\sin 2 \theta = \frac { 12 } { 13 }$

Question

Use the figure below to determine the exact value of the given function. $\sin 2 \theta$

A) $\sin 2 \theta = \frac { 5 } { 13 }$ 
B) $\sin 2 \theta = \frac { 7 } { 13 }$ 
C) $\sin 2 \theta = \frac { 12 } { 5 }$ 
D) $\sin 2 \theta = \frac { 9 } { 13 }$ 
E) $\sin 2 \theta = \frac { 12 } { 13 }$

Quizplus · Accepted Answer

From the right triangle in the diagram, we have $\sin 2	heta = \frac{BC}{AC}$. Using the Pythagorean Theorem, we have $AC^2 = 5^2+12^2=169$, so $AC = 13$. Using the triangle again, we have $BC = 12$, so $\sin 2	heta = \frac{12}{13}$. Therefore, the answer is $\boxed{	ext{(E)}}$.

Use the Figure Below to Determine the Exact Value of the Given