Use a half-angle identity to find the exact value of $\cos 105^{\circ }$ in simplest radical form.

An angle $\theta$ satisfies $\frac{\pi }{2}<\theta <\pi$. Which sign does the half-angle formula for $\sin \frac{\theta }{2}$ take, and why?

Use a half-angle identity to find the exact value of $\cos 157.5^{\circ }$ in simplest radical form.

An angle $\theta$ satisfies $\frac{3\pi }{2}<\theta <2\pi$. Which sign does the half-angle formula for $\sin \frac{\theta }{2}$ take, and why?

It is given that $\cos \theta =\frac{12}{13}$ and that $\theta$ lies in the first quadrant. Find the exact value of $\sin \frac{\theta }{2}$ in simplest radical form.

It is given that $\cos \theta =\frac{21}{29}$ and that $\theta$ lies in the first quadrant. Find the exact value of $\sin \frac{\theta }{2}$ in simplest radical form.

Use a half-angle identity to find the exact value of $\sin 112.5^{\circ }$ in simplest radical form.

An angle $\theta$ satisfies $\pi <\theta <\frac{3\pi }{2}$. Which sign does the half-angle formula for $\cos \frac{\theta }{2}$ take, and why?

It is given that $\cos \theta =-\frac{12}{13}$ and that $\theta$ lies in the second quadrant. Find the exact value of $\cos \frac{\theta }{2}$ in simplest radical form.

Which single trigonometric value is equal to $\sqrt{\frac{1+\cos \frac{\pi }{2}}{2}}$?

It is given that $\cos \theta =-\frac{24}{25}$ and that $\theta$ lies in the second quadrant. Find the exact value of $\sin \frac{\theta }{2}$ in simplest radical form.

Use a half-angle identity to find the exact value of $\cos 165^{\circ }$ in simplest radical form.

Which single trigonometric value is equal to $\sqrt{\frac{1-\cos \frac{3\pi }{2}}{2}}$?

It is given that $\cos \alpha =-\frac{3}{5}$, $\sin \alpha =\frac{4}{5}$, and $\alpha$ lies in the second quadrant. Use $\tan \frac{\alpha }{2}=\frac{\sin \alpha }{1+\cos \alpha }$ to find the exact value of $\tan \frac{\alpha }{2}$.

Which single trigonometric value is equal to $\sqrt{\frac{1+\cos \frac{2\pi }{3}}{2}}$?

Use a half-angle identity to find the exact value of $\cos 75^{\circ }$ in simplest radical form.

An angle $\theta$ satisfies $\frac{\pi }{2}<\theta <\pi$. Which sign does the half-angle formula for $\tan \frac{\theta }{2}$ take, and why?

Which single trigonometric value is equal to $\sqrt{\frac{1-\cos \frac{2\pi }{3}}{2}}$?

An angle $\theta$ satisfies $0<\theta <\frac{\pi }{2}$. Which sign does the half-angle formula for $\cos \frac{\theta }{2}$ take, and why?

Which single trigonometric value is equal to $\sqrt{\frac{1-\cos \frac{\pi }{2}}{2}}$?

Which single trigonometric value is equal to $\sqrt{\frac{1-\cos \frac{\pi }{3}}{2}}$?

Use a half-angle identity to find the exact value of $\sin 15^{\circ }$ in simplest radical form.

It is given that $\cos \theta =\frac{4}{5}$ and that $\theta$ lies in the first quadrant. Find the exact value of $\sin \frac{\theta }{2}$ in simplest radical form.

An angle $\theta$ satisfies $\pi <\theta <\frac{3\pi }{2}$. Which sign does the half-angle formula for $\tan \frac{\theta }{2}$ take, and why?

Which single trigonometric value is equal to $-\sqrt{\frac{1+\cos \frac{3\pi }{2}}{2}}$?

It is given that $\cos \theta =-\frac{12}{13}$ and that $\theta$ lies in the second quadrant. Find the exact value of $\sin \frac{\theta }{2}$ in simplest radical form.

An angle $\theta$ satisfies $\frac{3\pi }{2}<\theta <2\pi$. Which sign does the half-angle formula for $\cos \frac{\theta }{2}$ take, and why?

An angle $\theta$ satisfies $\frac{3\pi }{2}<\theta <2\pi$. Which sign does the half-angle formula for $\tan \frac{\theta }{2}$ take, and why?

Use a half-angle identity to find the exact value of $\sin 22.5^{\circ }$ in simplest radical form.

Which expression is a correct half-angle form for $\tan \frac{\theta }{2}$?

Use a half-angle identity to find the exact value of $\cos 15^{\circ }$ in simplest radical form.

Use a half-angle identity to find the exact value of $\sin 105^{\circ }$ in simplest radical form.

It is given that $\cos u=\frac{3}{5}$, $\sin u=\frac{4}{5}$, and $u$ lies in the first quadrant. Use a half-angle identity to find the exact value of $\tan \frac{u}{2}$.

Use a half-angle identity to find the exact value of $\tan 15^{\circ }$ in simplest radical form.

Use a half-angle identity to find the exact value of $\cos 112.5^{\circ }$ in simplest radical form.

Which expression is a correct half-angle form for $\tan \frac{\theta }{2}$?

Which expression is a correct half-angle form for $\tan \frac{\theta }{2}$?

Which single trigonometric value is equal to $-\sqrt{\frac{1+\cos \frac{5\pi }{3}}{2}}$?

It is given that $\cos \theta =-\frac{15}{17}$ and that $\theta$ lies in the second quadrant. Find the exact value of $\cos \frac{\theta }{2}$ in simplest radical form.

It is given that $\cos \theta =\frac{15}{17}$ and that $\theta$ lies in the first quadrant. Find the exact value of $\cos \frac{\theta }{2}$ in simplest radical form.