Write the function in the form \( y=a \sin b(x-c) \) or \( y=a \cos b(x-c) \). Find the period and phase shift. \( y=4 \cos \left(5 x+\frac{\pi}{6}\right) \)

Evaluate the expression \( \sin ^{-1}\left(\cos \left(\frac{7 \pi}{6}\right)\right) \)

Simplify \( \frac{\cos ^{2}(t)}{\sin ^{2}(t)+\cos ^{2}(t)} \) to an expression involving a single trig function with no fractions.

Simplify \( \frac{1+\cot (t)}{1+\tan (t)} \) to a single trig function with no fractions.

Find a simplified expression for \( \tan \left(\sin ^{-1}\left(\frac{x}{3}\right)\right) \)

Determine the value of \( \sin ^{2} x+\cos ^{2} x \) for \( x=15 \) degrees.