Warm up question
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Warm-Up Question. Solve each triangle. B. B. 10.8. 5. a. a. A. A. b. C. C. b. Definition of General Angles and Radian Measure. Trigonometric Ratios and Functions. Angles in Standard Position. Lesson: P.563. In a coordinate plane, an angle can be formed

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Warm-Up Question

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Warm up question

Warm-Up Question

Solve each triangle.

B

B

10.8

5

a

a

A

A

b

C

C

b


Definition of general angles and radian measure

Definition of General Anglesand Radian Measure

Trigonometric Ratiosand Functions


Angles in standard position

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.5663, 4, 6, 7, 8, 9, 14


Coterminal angles

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.56715, 16, 17, 18


Warm up question1

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

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.5655, 6, 7, 8


Radian measure1

Radian Measure


Arc length and area of a sector

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


Homework

Homework

Part 1

Workbook P.116: 1, 4, 5

Part 2

Workbook P.116 – 117: 6, 7, 8, 9, 10, 11, 13, 14


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