Section 1
Angles
In Exercises $1-4,$ find the indicated angles in the given examples of this section.In Example $1,$ find another angle that is coterminal with the given angle.
In Exercises $1-4,$ find the indicated angles in the given examples of this section.In Example $3,$ change $53^{\prime}$ to $35^{\prime}$ and then find the decimal form.
In Exercises $1-4,$ find the indicated angles in the given examples of this section.In Example $4,$ find another standard-position angle that has the same terminal side as the angle in Fig. $4.8(\mathrm{c})$
In Exercises $1-4,$ find the indicated angles in the given examples of this section.In Example $4,$ find another standard-position angle that has the same terminal side as the angle in Fig. $4.8(e)$
In Exercises $5-8,$ draw the given angles in standard position.$$60^{\circ}, 120^{\circ},-90^{\circ}$$
In Exercises $5-8,$ draw the given angles in standard position.$$330^{\circ},-150^{\circ}, 450^{\circ}$$
In Exercises $5-8,$ draw the given angles in standard position.$$50^{\circ},-120^{\circ},-30^{\circ}$$
In Exercises $5-8,$ draw the given angles in standard position.$$45^{\circ}, 245^{\circ},-250^{\circ}$$
In Exercises $9-14,$ determine one positive and one negative coterminal angle for each angle given.$$125^{\circ}$$
In Exercises $9-14,$ determine one positive and one negative coterminal angle for each angle given.$$173^{\circ}$$
In Exercises $9-14,$ determine one positive and one negative coterminal angle for each angle given.$$-150^{\circ}$$
In Exercises $9-14,$ determine one positive and one negative coterminal angle for each angle given.$$462^{\circ}$$
In Exercises $9-14,$ determine one positive and one negative coterminal angle for each angle given.$$278.1^{\circ}$$
In Exercises $9-14,$ determine one positive and one negative coterminal angle for each angle given.$$-197.6^{\circ}$$
In Exercises $15-18,$ by means of the definition of a radian, change the given angles in radians to equal angles expressed in degrees to the nearest $0.01^{\circ}$.0.675 rad
In Exercises $15-18,$ by means of the definition of a radian, change the given angles in radians to equal angles expressed in degrees to the nearest $0.01^{\circ}$.$$0.838 \mathrm{rad}$$
In Exercises $15-18,$ 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 rad
In Exercises $15-18,$ 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 rad
In Exercises $19-22,$ use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest $0.01^{\circ}$.$$1.257 \mathrm{rad}$$
In Exercises $19-22,$ use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest $0.01^{\circ}$.$$2.089 \mathrm{rad}$$
In Exercises $19-22,$ use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest $0.01^{\circ}$.$$-4.110 \mathrm{rad}$$
In Exercises $19-22,$ 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
In Exercises $23-26,$ use a calculator conversion sequence to change the given angles to equal angles expressed in radians to three significant digits.$$85.0^{\circ}$$
In Exercises $23-26,$ use a calculator conversion sequence to change the given angles to equal angles expressed in radians to three significant digits.$$237.4^{\circ}$$
In Exercises $23-26,$ use a calculator conversion sequence to change the given angles to equal angles expressed in radians to three significant digits.$$384.8^{\circ}$$
In Exercises $23-26,$ use a calculator conversion sequence to change the given angles to equal angles expressed in radians to three significant digits.$$-117.5^{\circ}$$
In Exercises $27-30,$ change the given angles to equal angles expressed to the nearest minute.$$47.50^{\circ}$$
In Exercises $27-30,$ change the given angles to equal angles expressed to the nearest minute.$$715.80^{\circ}$$
In Exercises $27-30,$ change the given angles to equal angles expressed to the nearest minute.$$-5.62^{\circ}$$
In Exercises $27-30,$ change the given angles to equal angles expressed to the nearest minute.$$142.87^{\circ}$$
In Exercises $31-34,$ change the given angles to equal angles expressed in decimal form to the nearest $0.01^{\circ} .$$$15^{\circ} 12^{\prime}$$
In Exercises $31-34,$ change the given angles to equal angles expressed in decimal form to the nearest $0.01^{\circ} .$$$517^{\circ} 39^{\prime}$$
In Exercises $31-34,$ change the given angles to equal angles expressed in decimal form to the nearest $0.01^{\circ} .$$$301^{\circ} 16^{\prime}$$
In Exercises $31-34,$ change the given angles to equal angles expressed in decimal form to the nearest $0.01^{\circ} .$$$-94^{\circ} 47^{\prime}$$
In Exercises $35-42,$ draw angles in standard position such that the terminal side passes through the given point.$$(4,2)$$
In Exercises $35-42,$ draw angles in standard position such that the terminal side passes through the given point.$$(-3,8)$$
In Exercises $35-42,$ draw angles in standard position such that the terminal side passes through the given point.$$(-3,-5)$$
In Exercises $35-42,$ draw angles in standard position such that the terminal side passes through the given point.$$(6,-1)$$
In Exercises $35-42,$ draw angles in standard position such that the terminal side passes through the given point.$$(-7,5)$$
In Exercises $35-42,$ draw angles in standard position such that the terminal side passes through the given point.$$(-4,-2)$$
In Exercises $35-42,$ draw angles in standard position such that the terminal side passes through the given point.$$(-2,0)$$
In Exercises $35-42,$ draw angles in standard position such that the terminal side passes through the given point.$$(0,6)$$
In Exercises $43-50$, the given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.$$31^{\circ}, 310^{\circ}$$
In Exercises $43-50$, the given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.$$180^{\circ}, 92^{\circ}$$
In Exercises $43-50$, the given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.$$435^{\circ},-270^{\circ}$$
In Exercises $43-50$, the given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.$$-5^{\circ}, 265^{\circ}$$
In Exercises $43-50$, the given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.$$1 \mathrm{rad}, 2 \mathrm{rad}$$
In Exercises $43-50$, the given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.$$3 \mathrm{rad},-3 \pi \mathrm{rad}$$
In Exercises $43-50$, the given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.$$4 \mathrm{rad}, \pi / 3 \mathrm{rad}$$
In Exercises $43-50$, the given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.$$12 \mathrm{rad},-2 \mathrm{rad}$$
In Exercises 51 and $52,$ change the given angles to equal angles expressed in decimal form to the nearest $0.001^{\circ} .$ In Exercises 53 and 54 change the given angles to equal angles expressed to the nearest second.$$21^{\circ} 42^{\prime} 36^{\prime \prime}$$
In Exercises 51 and $52,$ change the given angles to equal angles expressed in decimal form to the nearest $0.001^{\circ} .$ In Exercises 53 and 54 change the given angles to equal angles expressed to the nearest second.$$-107^{\circ} 16^{\prime} 23^{\prime \prime}$$
In Exercises 51 and $52,$ change the given angles to equal angles expressed in decimal form to the nearest $0.001^{\circ} .$ In Exercises 53 and 54 change the given angles to equal angles expressed to the nearest second.$$86.274^{\circ}$$
In Exercises 51 and $52,$ change the given angles to equal angles expressed in decimal form to the nearest $0.001^{\circ} .$ In Exercises 53 and 54 change the given angles to equal angles expressed to the nearest second.$$257.019^{\circ}$$
A circular gear rotates clockwise by exactly 3.5 revolutions. By how many degrees does it rotate?
A windmill rotates 15.6 revolutions in a counterclockwise direction. By how many radians does it rotate?