What is the period of y = sin x (the basic sine function)?

A transformed sine wave has a midline y = 3 and a crest at y = 7. What is the amplitude?

A sine-like graph has midline y = 2, amplitude 3, period π, and its first crest (peak) occurs at x = π/4. Construct an equation y = A sin(Bx − h) + D that matches this description.

Compute csc(π/6).

Find the vertical asymptotes of y = sec(3x) within one period in (0, π)).

y = tan((π/3)x) is horizontally shifted right by π/6. What is the period of the original tan((π/3)x), and how much horizontally do the vertical asymptotes move under the shift? (Describe the original period and the translation of asymptote positions.)

If $\sin \left(P\right)=\frac{1}{6}$ and $\cos \left(P\right)=\frac{\sqrt{35}}{6}$, find $\cot \left(P\right)$ using trigonometric identities.

Find the value of $\cos \frac{5\pi }{12}$ as $\cos (\frac{\pi }{6}+\frac{\pi }{4})$.

In a triangle, side $b$ is $5\text{ units}$ long and it faces angle $B$ which measures ${60}^{\circ }$. If angle $A$ is ${45}^{\circ }$, find the length of side $a$ opposite to angle $A$. Round your answer to two decimal places.

Evaluate $f^{\prime }\left(x\right)$ at $x=\frac{\pi }{4}$ if $f\left(x\right)=\cos x$.

Find the derivative of $y=\frac{\cos x}{2-\sin x}$.

Find the derivative of the function $y={\left(\frac{2\tan x}{1-\sin x}\right)}^{\frac{1}{2}}$.