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When in standard position, the terminal side of an angle intersects the unit circle at ${\displaystyle (\frac{5}{13},\frac{12}{13})}$. Describe sin (θ).  

find the exact value of $\tan (\frac{4\pi }{3}-\frac{\pi }{4})$

Find the linear equations that can be used to convert an (x, y) equation to a (x, v) equation using the given angle of rotation θ. 

$\theta ={70}^{\circ }$

Find the linear equations that can be used to convert an (x, y) equation to a (x, v) equation using the given angle of rotation θ.

$\theta =\frac{\pi }{3}$

Write an equation in terms of x and y for the function that is described by the given characteristics. A sine curve with a period of $\pi$, an amplitude of 3, a right phase shift of $\frac{\pi }{2}$, and a vertical translation up 2 units.

Prove that ${\displaystyle (1+\cos \theta )(1-\cos \theta )={\sin }^2\theta }$

The terminal side of an angle $\theta$ in standard position intersects the unit circle at ${\displaystyle (\frac{5}{13},\frac{12}{13})}$. What is $\sin (\theta )$?
Write your answer in simplified, rationalized form.

$\tan {28}^{\circ }=\cot ?$

If $A={40}^{\circ },B={60}^{\circ }$, and $a=20$, find b.

$\frac{\tan \alpha +\cot \alpha }{\sin \alpha -\cos \alpha }={\sec }^2\alpha +{\csc }^2\alpha$

${\displaystyle \sin \left(2{\cos }^{-1}\times \left(\frac{\sqrt{2}}{2}\right)\right)}$

Determine the surface for which the equation is given. $p=\sin \theta \sin \varphi$