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### Definition of General Anglesand Radian Measure

Trigonometric Ratiosand Functions

Angles in Standard Position

- Lesson: P.563

In a coordinate plane, an angle can be formed

by fixing one ray, called the initial side, and

rotating the other ray, called the terminal side,

about the vertex.

An angle is in standard position if its vertex is at

the origin and its initial side lies on the positive

x-axis.

terminal side

initial side

- Example: P.563

Draw an angle with the given measure in standard position.

Required Practice: P.566 3, 4, 6, 7, 8, 9, 14

Coterminal Angles

- Lesson: P.564

The angle and are coterminal because

their terminal sides coincide. An angle coterminal

with a given angle can be found by adding or

subtracting multiples of .

- Example: P.564

Draw an angle with the given measure in standard position. Then find one positive coterminal angel and one negative coterminal angle.

Required Practice: P.567 15, 16, 17, 18

Warm-Up Question

Find the circumference and area of below circle.

Circumference:

Area of Circle:

5

Find the arc length and area of below sector.

Arc Length:

5

Area of Sector:

Radian Measure

- Lesson: P.564

One radian is the measure of an angle in standard

position whose terminal side intercepts an arc of

length r. (Refer to the animation on the next slide.)

There are approximately 6.28 radian in a full circle,

or to be exact. Degree measure and radian

measure are therefore related by the equation

radians, or .

r

r

1 radian

- Example: P.564

Convert to radians.

Convert to degrees.

Required Practice: P.565 5, 6, 7, 8

Arc Length and Area of a Sector

- Lesson: P.565

The arc length s and area A of a sector with radius r

and central angle (measured in radians) are as

follows.

Arc Length:

Area:

sector

r

arc

length

s

central angleθ

- Example: P.567

Find the arc length and area of a sector with the given radius r and central angle .

1) r = 4 in., 2) r = 15 cm,

Required Practice: P.56733, 37

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