Chapter 4

Change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\) $$0.265 \mathrm{rad}$$

By means of the definition of a radian, change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\). $$0.265 rad$$

Change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\) $$0.838 \mathrm{rad}$$

By means of the definition of a radian, change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\). $$0.838 \mathrm{rad}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. A straight driveway is \(85.0 \mathrm{ft}\) long, and the top is \(12.0 \mathrm{ft}\) above the bottom. What angle does it make with the horizontal?

Find the values of the indicated functions. In Exercises \(17-20,\) give answers in exact form. In Exercises \(21-24,\) the values are approximate. Given \(\tan \theta=2,\) find \(\sin \theta\) and \(\sec \theta\).

Change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\) $$4.447 \mathrm{rad}$$

By means of the definition of a radian, change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\). $$4.447 \mathrm{rad}$$

Find the values of the indicated functions. In Exercises \(17-20,\) give answers in exact form. In Exercises \(21-24,\) the values are approximate. Given \(\sec \theta=\sqrt{5} / 2,\) find \(\tan \theta\) and \(\cos \theta\).

Change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\) $$-3.642 \mathrm{rad}$$

By means of the definition of a radian, change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\). $$-3.642 \mathrm{rad}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. The angle of inclination of a road is often expressed as percent grade, which is the vertical rise divided by the horizontal run (expressed as a percent). See Fig. 4.57. A 6.0\% grade corresponds to a road that rises \(6.0 \mathrm{ft}\) for every \(100 \mathrm{ft}\) along the horizontal. Find the angle of inclination that corresponds to a 6.0\% grade.

Find the values of the indicated functions. In Exercises \(17-20,\) give answers in exact form. In Exercises \(21-24,\) the values are approximate. Given \(\sin \theta=0.750,\) find \(\cot \theta\) and \(\csc \theta\).

Use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\) $$0.329 \mathrm{rad}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. A circular patio table of diameter \(1.20 \mathrm{m}\) has a regular octagon design inscribed within the outer edge (all eight vertices touch the circle). What is the perimeter of the octagon?

Use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\) $$2.089 \mathrm{rad}$$

Use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\) $$-4.110 \mathrm{rad}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. From a space probe circling Io, one of Jupiter's moons, at an altitude of \(552 \mathrm{km},\) it was observed that the angle of depression of the horizon was \(39.7^{\circ} .\) What is the radius of Io?

find the values of the indicated functions. In Exer. cises \(17-20,\) give answers in exact form. In Exercises \(21-24,\) the val. ues are approximate. Given \(\csc \theta=1.20,\) find \(\sec \theta\) and \(\cos \theta.\)

Use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\) $$6.705 rad$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. A manufacturing plant is designed to be in the shape of a regular pentagon with \(92.5 \mathrm{ft}\) on each side. A security fence surrounds the building to form a circle, and each corner of the building is to be \(25.0 \mathrm{ft}\) from the closest point on the fence. How much fencing is required?

Each given point is on the terminal side of an angle. Show that each of the given ficnctions is the same for each points. \((3,4),(6,8),(4.5,6), \sin \theta\) and \(\tan \theta.\)

Use a calculator conversion sequence to change the given angles to equal angles expressed in radians to three significant digits. $$56.0^{\circ}$$

Use a calculator conversion sequence to change the given angles to equal angles expressed in radians to three significant digits. $$237.4^{\circ}$$

Each given point is on the terminal side of an angle. Show that each of the given functions is the same for each points. \((0.3,0.1),(9,3),(33,11), \tan \theta\) and \(\sec \theta\)

Use a calculator conversion sequence to change the given angles to equal angles expressed in radians to three significant digits. $$384.8^{\circ}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. What is the circumference of the Arctic Circle (latitude \(\left.66^{\circ} 32^{\prime} \mathrm{N}\right) ?\) The radius of the earth is 3960 mi.

Each given point is on the terminal side of an angle. Show that each of the given functions is the same for each points. \((40,30),(56,42),(36,27), \csc \theta\) and \(\cos \theta\)

Use a calculator conversion sequence to change the given angles to equal angles expressed in radians to three significant digits. $$-117.5^{\circ}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. A draftsman sets the legs of a pair of dividers so that the angle between them is \(32.0^{\circ} .\) If each leg is 4.50 in. long. what is the distance between their ends where they touch the paper?

Change the given angles to equal angles expressed to the nearest minute. $$47.50^{\circ}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. The ratio of the width to the height of a TV screen is 16 to 9 What is the angle between the width and a diagonal of the screen?

Change the given angles to equal angles expressed to the nearest minute. $$715.80^{\circ}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. When the distance from Earth to the sun is 94,500,000 mi, the angle that the sun subtends on Earth is \(0.522^{\circ} .\) Find the diameter of the sun.

Answer the given questions. For an acute angle \(A,\) which is greater, \(\sin A\) or \(\tan A ?\)

Change the given angles to equal angles expressed to the nearest minute. $$-5.62^{\circ}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. Two ladders, each \(6.50 \mathrm{m}\) long are leaning against opposite walls of a level alley, with their feet touching. If they make angles of \(38.0^{\circ}\) and \(68.0^{\circ}\) with respect to the alley floor, how wide is the alley?

Answer the given questions. For an acute angle \(A > 45^{\circ},\) which is less, tan \(A\) or \(\cot A ?\)

Answer the given questions. For an acute angle \(A>45^{\circ},\) which is less, tan \(A\) or cot \(A ?\)

Change the given angles to equal angles expressed to the nearest minute. $$142.87^{\circ}$$

Answer the given questions. If \(\tan \theta=3 / 4,\) what is the value of \(\sin ^{2} \theta+\cos ^{2} \theta ?\) \(\left[\sin ^{2} \theta=(\sin \theta)^{2}\right]\)

Change the given angles to equal angles expressed in decimal form to the nearest \(0.01^{\circ}\) $$15^{\circ} 12^{\prime}$$

Answer the given questions. If \(\sin \theta=2 / 3,\) what is the value of \(\sec ^{2} \theta-\tan ^{2} \theta ?\)

Change the given angles to equal angles expressed in decimal form to the nearest \(0.01^{\circ}\) $$517^{\circ} 39^{\prime}$$

Answer the given questions. If \(y=\sin \theta,\) what is \(\cos \theta\) in terms of \(y ?\)

Change the given angles to equal angles expressed in decimal form to the nearest \(0.01^{\circ}\) $$301^{\circ} 16^{\prime}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. An antenna was on the top of the World Trade Center (before it was destroyed in 2001 ). From a point on the river 7800 ft from the Center, the angles of elevation of the top and bottom of the antenna were \(12.1^{\circ}\) and \(9.9^{\circ},\) respectively. How tall was the antenna? (Disregard the small part of the antenna near the base that could not be seen.) The former World Trade Center is shown in Fig. 4.64. (This problem is included in memory of those who suffered and died as a result of the terrorist attack of September \(11,2001 .)\)

Answer the given questions. If \(x=\cos \theta,\) what is \(\tan \theta\) in terms of \(x ?\)

Change the given angles to equal angles expressed in decimal form to the nearest \(0.01^{\circ}\) $$-94^{\circ} 47^{\prime}$$

Find the indicated part of the right triangle that has the given parts. One leg is \(25.6,\) and the hypotenuse is \(37.5 .\) Find the smaller acute angle.