L.S. \( \frac{\sin \theta \cos \theta}{1+\cos \theta}-\frac{\sin \theta}{1-\cos \theta}=-(\cot \theta \cos \theta+\csc \theta) \) \( (1+\cos \theta)(1-\cos \theta) \)

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.)

Calcule tanx cuando la expresión \( 5\left(\sqrt{3} \cos 7^{\circ}-\operatorname{sen} 7^{\circ}\right) \cos x+15 \operatorname{sen} x \) toma su máximo valor.

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.)

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. \( \begin{array}{l}y=\square \sin (\square x-\square) \\ \text { (Use integers or fractions for any numbers in the expression. Simplify your answers.) }\end{array} \)

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.)