2. a) Verify that \( \frac{\cos x}{1-\sin x}=\frac{1+\sin x}{\cos x} \) is true for \( x=\frac{\pi}{4} \). b) What are the non-permissible values for the equation?

Determine the period of the function \( f(x)=2 \cos \left(\frac{1}{6} x+\frac{\pi}{3}\right) \). (1 point) \( -\frac{\pi}{3} \) \( \frac{\pi}{3} \) \( 2 \pi \) \( 12 \pi \)

If the cosine function is stretched by a factor of 10 , what will the resulting function \( f(x) \) be? (1 point) \( f(x)=\cos (10 x) \) \( f(x)=\cos (20 x) \) \( f(x)=\cos \left(\frac{x}{10}\right) \) \( f(x)=\cos \left(\frac{x}{20}\right) \)

A periodic function passes through the origin and then descends to a minimum of \( -\frac{2}{3} \) when \( x=\frac{\pi}{2} \). It passes through the x-axis again when \( x=\pi \) and rises to a maximum of \( \frac{2}{3} \) when periodic function? (1 point) \( y=-\frac{2}{3} \cos x \) \( y=\frac{2}{3} \sin x \) \( y=\frac{4}{3} \sin x \) \( y=-\frac{2}{3} \sin x \)

When the function \( f(x)= \) sin \( x \) is reflected across the \( y \)-axis, identify the coordinates of the reflected point of \( \left(\frac{\pi}{2}, 1\right) \) across the \( y \)-axis. (1 point) \( \left(\frac{-\pi}{2},-1\right) \) \( \left(\frac{-\pi}{2}, 1\right) \) \( \left(\frac{\pi}{2},-1\right) \) \( \left(\frac{\pi}{2}, 1\right) \)

Find the height of a tree if the angle of elevation to its topmost part changes from \( 25^{\circ} \) to \( 45^{\circ} \) as the observer moves 10 m closert to the base of the tree.