Complete the identity.
-$\sin ( 4 \theta ) = ?$
A) $1 - 8 \sin ^ { 2 } \theta \cos ^ { 2 } \theta$
B) $4 \sin \theta \cos ^ { 3 } \theta - 4 \sin ^ { 3 } \theta \cos \theta$
C) $3 \sin \theta - 4 \sin ^ { 3 } \theta$
D) $\cos ^ { 3 } \theta - 3 \sin ^ { 2 } \theta \cos \theta$

Question

Quizplus · Accepted Answer

The correct identity for $\sin(4\theta)$ is derived from the double angle formulas for sine and cosine, ultimately simplifying to $4 \sin \theta \cos ^ { 3 } \theta - 4 \sin ^ { 3 } \theta \cos \theta$, which matches option B.

Complete the Identity sin⁡(4θ)=?\sin ( 4 \theta ) = ?sin(4θ)=? A) 1−8sin⁡2θcos⁡2θ1 - 8 \sin ^ { 2 } \theta \cos ^ { 2 } \theta1−8sin2θcos2θ

Complete the Identity $\sin ( 4 \theta ) = ?$ A) $1 - 8 \sin ^ { 2 } \theta \cos ^ { 2 } \theta$