Trigonometric and Polar Functions

Given $p(y)=\frac{\sec(y- \pi/6)}{\cos(y-\pi/6)}$, what values of $y$ would potentially cause a discontinuity in $p(y)$?

If the function $f(x) = 2\sin(3x)$ has an inverse, which of the following represents the domain of $f^{-1}(x)$?

If the graph of $y = \\sin(x)$ is transformed by a vertical stretch by a factor of 3 and then shifted up 2 units, which equation represents the new graph?

What is the period change in the graph $y = \\csc(x) + 4$ from its parent function due to transformations?

If a trigonometric function $h(\theta)$ has a vertical asymptote at $\theta = k\pi$ where $k$ is an integer, how does it affect the continuity of $h(\theta)$?

If $\cos(\theta) = \frac{1}{4}$ and $\theta$ is in the first quadrant, what is the value of $\tan(\theta)$?

What is the value of $\sin(x) \times \cos(x)$ at $x = \frac{5\pi}{4}$?

What is the amplitude of the trigonometric function $y = 3 ext{sin}(x)$?

What must be true about angle ϕ for cos(ϕ) to equal its own Taylor series expansion at all real numbers?

Which expression is equivalent to $\\sin(2x)$ using the double-angle formula?