Exam 1: Trigonometry

A 50-meter line is used to tether a helium-filled balloon.Because of a breeze, the line makes an angle of approximately 55° with the ground.What is the height of the balloon? (Round the answer to one decimal place.) ​

Describe the behavior of the function below as x approaches zero. ​ ​

A passenger in an airplane at an altitude of a = 20 kilometers sees two towns directly to the east of the plane.The angles of depression to the towns are 28º and 55º (see figure).How far apart are the towns? How far apart are the ships? Round your answer to one decimal place. ​ ​

Find the area of the sector of the circle with radius r and central angle θ.Round to two decimal places. ​ Radius r Central Angle θ ​4 inches ​ ​

The height of an outdoor basketball backboard is feet, and the backboard casts a shadow feet long. Find the angle of elevation of the sun.Round your answer to one decimal place. ​

Find the value of the expression.Round your result to two decimal places. ​ ​

Find the point (x, y) on the unit circle that corresponds to the real number t. ​ ​

Find the length of the sides of a regular hexagon inscribed in a circle of radius 29 inches. ​

An engineer erects a 111-foot cellular telephone tower.Find the angle of elevation to the top of the tower at a point on level ground 62 feet from its base.Round your answer to one decimal place. ​

Using the figure below, if θ = 20° and y = 16, determine the exact value of r.

Use an inverse function to write θ as a function of x.

Find the point on the unit circle that corresponds to the real number .Use your results to evaluate .

You are holding one of the tethers attached to the top of a giant character balloon in a parade.Before the start of the parade the balloon is upright and the bottom is floating approximately 20 feet above ground level.You are standing approximately a = 130 feet ahead of the balloon (see figure). ​ ​ Find the length l of the tether you are holding in terms of h, the height h of the balloon from top to bottom. ​

For a person at rest, the velocity v (in liters per second) of airflow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is given by ​ , ​ Where t is the time (in seconds). (Inhalation occurs when v > 0 and exhalation occurs when v < 0.) Select the graph of this velocity function. ​

If and , determine the value of B.Round to two decimal places.

Use a calculator to evaluate tan 49°34´.Round your answer to four decimal places.

Use an inverse trigonometric function to write θ as a function of x. ​ ​ A = x B = 6 ​

Evaluate each function.Round your answers to four decimal places. ​ Sec48°38' and csc31°57' ​

Use the properties of inverse trigonometric functions to evaluate the expression. ​ ​

Rewrite in degree measure.Round to three decimal places.