Find $\sin \theta$ And $\cos \theta$ , Where $\theta$ Is the (Acute) Angle of Rotation That Eliminates The

Multiple Choice

Find $\sin \theta$ and $\cos \theta$ , where $\theta$ is the (acute) angle of rotation that eliminates the $x ^ { \prime } y ^ { \prime }$ -term. Note: You are not asked to graph the equation. $124 x ^ { 2 } + 7 x y + 100 y ^ { 2 } = 0$

A) $\sin \theta = \frac { 7 \sqrt { 2 } } { 26 }$ $\cos \theta = \frac { 17 \sqrt { 2 } } { 26 }$
B) $\sin \theta = \frac { \sqrt { 2 } } { 10 }$ $\cos \theta = \frac { 17 \sqrt { 2 } } { 26 }$
C) $\sin \theta = \frac { \sqrt { 2 } } { 10 }$ $\cos \theta = \frac { 7 \sqrt { 2 } } { 10 }$
D) $\sin \theta = \frac { 17 \sqrt { 2 } } { 26 }$ $\cos \theta = \frac { 7 \sqrt { 2 } } { 26 }$
E) $\sin \theta = \frac { 7 \sqrt { 2 } } { 10 }$ $\cos \theta = \frac { \sqrt { 2 } } { 10 }$