Exam 6: The Trigonometric Functions

An airplane flying at a speed of 360 mi/hr flies from a point A in the direction for 15 minutes and then flies in the direction for 30 minutes. Approximate, to the nearest mile, the distance from the airplane to A.

Points on the terminal sides of angles play an important part in the design of arms for robots. Suppose a robot has a straight arm 18 inches long that can rotate about the origin in a coordinate plane. If the robot's hand is located at (18, 0) and then rotates through an angle of 60 ^o , what is the new location of the hand?

Approximate, to the nearest 0.01 radian, all angles in the interval [ 0, 2 ) that satisfy the equation. = 0.2518

Find y by referring to the graph of the trigonometric function.

A CB antenna is located on the top of a garage that is 17 feet tall. From a point on level ground that is 120 feet from a point directly below the antenna, the antenna subtends an angle of , as shown in the figure. Approximate the length of the antenna. Give the answer to one decimal place.

Find the quadrant containing if the given conditions are true. and

Approximate, to the nearest 0.01 radian, all angles in the interval [ 0, 2 ) that satisfy the equation. = 0.8412

Approximate the acute angle to the nearest .

Sketch the graph of the equation.

Let P ( t ) be the point on the unit circle U that corresponds to t. If P ( t ) has the coordinates , find , , , .

A ladder 18 feet long leans against the side of a building, and the angle between the ladder and the building is . A. Approximate the distance from the bottom of the ladder to the building. Give the answer to one decimal place. B. If the distance from the bottom of the ladder to the building is increased by 2 feet, approximately how far does the top of the ladder move down the building? Give the answer to one decimal place.

Express the angle as a decimal, to the nearest ten-thousandth of a degree.

Let P ( t ) be the point on the unit circle U that corresponds to t. If P ( t ) has the coordinates , find , , , .

Points on the terminal sides of angles play an important part in the design of arms for robots. Suppose a robot has a straight arm 16 inches long that can rotate about the origin in a coordinate plane. If the robot's hand is located at (16, 0) and then rotates through an angle of 60 ^o , what is the new location of the hand?

Express = 4.5 in terms of degrees, minutes, and seconds, to the nearest second.

Express = 2.5 in terms of degrees, minutes, and seconds, to the nearest second.

Radio stations often have more than one broadcasting tower because federal guidelines do not usually permit a radio station to broadcast its signal in all directions with equal power. Since radio waves can travel over long distances, it is important to control their directional patterns so that radio stations do not interfere with one another. Suppose that a radio station has two broadcasting towers located along a north-south line, as shown in the figure. If the radio station is broadcasting at a wavelength and the distance between the two radio towers is equal to , then the intensity I of the signal in the direction is given by where I _o is the maximum intensity. Approximate I in terms of I _o for .

Scientists sometimes use the formula to simulate temperature variations during the day, with time t in hours, temperature f ( t ) in , and t=0 corresponding to midnight. Assume that f ( t ) is decreasing at midnight. Determine values of a, b, c, and d that fit the information: the high temperature is 17 , and the low temperature of -17 occurs at 4 A.M.

If a circular arc of the length s = 16 cm subtends the central angle = 2 on a circle, find the radius of the circle.

Rewrite the expression in nonradical form without using absolute values for the indicated values of . ;