Write the given expression as a single trigonometric ratio.

$2\sin 4\pi \cos 4\pi$

Write the given expression as a single trigonometric ratio.

${\cos }^{2}0.4-{\sin }^{2}0.4$

Write the given expression as a single trigonometric ratio.

$2{\cos }^2\left(6\right)-1$

Write the given expression as a single trigonometric ratio.

$1-2{\sin }^2\frac{\pi }{4}$

Given that $\sin \theta =\frac{1}{3}$ and $\theta$ is acute, evaluate the given expression.

$\cos \theta$

Given that $\sin \theta =\frac{1}{3}$ and $\theta$ is acute, evaluate the given expression.

$\sin 2\theta$

Given that $\sin \theta =\frac{1}{3}$ and $\theta$ is acute, evaluate the given expression.

$\cos 2\theta$

Given that $\sin \theta =\frac{1}{3}$ and $\theta$ is acute, evaluate the given expression.

$\tan 2\theta$

Given that $\cos \theta =-\frac{1}{2}$, and $\theta$ is obtuse, find:

$\sin \theta$