Use a sum-to-product formula to rewrite \( \sin 4 z+\sin 3 z \) as a product. \( \sin 4 z+\sin 3 z=\square \)

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. (Type an integer or a fraction.) B. The amplitude does not exist. The period of \( y=3 \) tan \( (6 x-\pi) \) is (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any numbers in the expression.)

Write the equation of a sine function that has the following characteristics. Amplitude: \( 9 \quad \) Period: \( 7 \pi \quad \) Phase shift: \( \frac{1}{2} \) Type the appropriate values to complete the sine function. \( \begin{array}{l}y=\square \sin (\square x-\square) \\ \text { (Use integers or fractions for any numbers in the expression. Simplify your answers.) }\end{array} \)

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 tower that is 102 feet tall casts a shadow 117 feet long. Find the angle of elevation of the sun to the nearest degree. The angle of elevation is \( \square \) degrees. (Round to the nearest degree.)

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.)