Find the amplitude (if one exists), period, and phase shift of the following function. Graph the function. Be sure to label key points. Show at least two periods. \[ y=3 \tan (6 x-\pi) \] What is the amplitude of \( y=3 \tan (6 x-\pi) \) ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The amplitude is (Type an integer or a fraction.) B. The amplitude does not exist.

A funicular carries passengers up an embankment to an observation point. If the length of the track is 67.8 meters and the angle of inclination is \( 39^{\circ} 4^{\prime} \), determine the height of the embankment. The embankment is \( \square \) meters high. (Round to two decimal places as needed.)

The angle of elevation of the Sun is \( 33.1^{\circ} \) at the instant the shadow cast by a monument is 720 feet long. Use this information to calculate the height of the monument. The height of the monument is \( \square \mathrm{ft} \). (Round to two decimal places as needed.)

-pi/3 on the unit circle

Write the equation of a sine function that has the following characteristics. \[ \begin{array}{l}\text { Amplitude: } 3 \text { Period: } 9 \pi \quad \text { Phase shift: }-\frac{1}{4} \\ \text { Type the appropriate values to complete the sine function. } \\ \begin{array}{l}y=\square \sin (\square x+\square) \\ \\ \text { (Use integers or fractions for any numbers in the expression. Simplify your answers.) }\end{array}\end{array} . \begin{array}{l}\square\end{array} \]

Si se cumple que \( \tan ^{2} x=2+3 \tan ^{2} y \), calcule el valor de la siguiente expresión. \( \frac{1-\cos (x+y) \cos (x-y)}{\operatorname{sen}(x+y) \operatorname{sen}(x-y)-1} \)