Section 5.1

Angles and Their Measure

HW concepts/vocab; 4-44 M4;

86,87,91,96,99,104

Reading anglesFormerly Capital Letters…

but now Greek Letters

Alpha αBeta β

Gamma γTheta θ

Omega ω

Angle Classification

• By size– Acute– Right– Obtuse– Straight– Reflex– Coterminal

• By location when initial ray is on the positive x-axis– Quad I, II, III, or IV– Quadrantal if terminal

ray is on the x or y-axis

OBJECTIVE 1

(a) Convert 45 10'15" to decimal in degrees.

Round the answer to four decimal places.

(b) Convert 21.256 to the D M'S" form.

Round the answer to the nearest second.

The Unit Circle

210 ْ

Radians

OBJECTIVE 2

Find the length of the arc of a circle of radius 4 meters subtended by a central angle of 0.5 radian.

OBJECTIVE 3

(a) 80° (b) 140° (c) -30° (d) 100°

2 5 3(a) radians (b) radians (c) radians

3 6 5

8(d) radians (e) 2 radians

3

OBJECTIVE 4

Find the area of the sector of a circle of radius 5 feet formed by an angle of 40°..

OBJECTIVE 5

Linear Speed

Angular Speed

Earth rotates on an axis through its poles. The distance from the axis to a location on Earth 40° north latitude is about 3033.5 miles. Therefore, a location on Earth at 40° north latitude is spinning on a circle of radius 3033.5 miles. Compute the linear speed on the surface of Earth at 40° north latitude.

The propellers on an average freighter have a radius of 4 feet. At full speed ahead, the propellers turn at 150 rpm.

a. Find the angular velocity in radians per minute at the tip of the blade.

At the center of the blade?

b. Find the linear velocity in feet/minute at the tip of the blade? At the center of the propeller?

Dan Druff and Ella Funt are riding on a Ferris Wheel. Dan observes that ittakes 20 seconds to make a complete revolution. Their seat is 25 feet from the axle of the wheel.

a. What is their angular velocity in revolutions per minute? b. Degrees per minute? c. Radians per minute?d. What is their linear velocity?

Della Casee is riding a racing bike at a speed of 50.4 km/h. The wheels have a diameter of 70 cm.Find the angular velocity of the wheels in radians per second.