Simplify \( \frac{\csc ^{2}(t)-1}{\csc ^{2}(t)} \) to an expression involving a single trig function with no fractions. If needed, enter squared trigonometric expressions using the following notation. Example: Enter \( \sin ^{2}(t) \) as \( (\sin (t))^{2} \).

Tom wants to clean his second story windows and plans to buy a ladder that will reach at least 20 feet high. If he leans the ladder against the house so that the base of the ladder makes a 59 degree angle with the ground, how long of a ladder should he buy? Round to a whole number as necessary. The ladder length is \( \square \) feet. (Round to a whole number as needed.)

Identify the transformations for the function \( f(x)=3 \cos \left(-x+\frac{\pi}{3}\right)-2 \). ( 1 point) vertical stretch by a factor of 3 , reflection over the \( y \)-axis, horizontal shift right by \( \frac{\pi}{3} \), and vertical shift down 2 vertical stretch by a factor of 3 , reflection over the \( y \)-axis, horizontal shift right by \( \frac{\pi}{3} \), and vertical shift up 2 vertical stretch by a factor of 3 , horizontal compression by -1 , horizontal shift night by \( \frac{\pi}{3} \), and . vertical shift down 2 vertical stretch by a factor of 3 , reflection over the \( y \)-axis, horizontal shift left by \( \frac{\pi}{3} \), and vertical shift down 2

Find the period and write the equation of the sine function that has a maximum at \( \left(\frac{\pi}{14}, 1\right) \) and a minimum at \( \left(\frac{3 \pi}{14},-1\right) \). (1 point) period \( =\square \) \( f(x)=\sin (\square) \)

\( 179 ^ { \circ } 59 ^ { \prime } 60 ^ { \prime \prime } - 103 ^ { \circ } 31 ^ { \prime } 14 ^ { \prime \prime } \)

If \( \tan \left(3 \theta-70^{\circ}\right) \times \tan \theta=1 \) where \( \left.\theta \in\right] 0, \frac{\pi}{3}[ \), then \( \sin (2 \theta+10)= \)