DO NOW

• Pick up a folder off the table and write your name on the tab.

• This is the folder you will turn all quizzes and tests into.

• It will be alphabetically placed in the top drawer of the filing cabinet.

ConversionsRadians to DegreesDegrees to Radians

Use the Calculator• Find the following to the 4 decimal places• Make sure your calculator is in radian mode or

degree mode. • Use correct mode or your answer will be

wrong! Mode• Sin 2.34R = radians• Cos 5π/8 = radians• Tan 125° = degrees• Csc 3π/5 = radians• Cot 48° = degrees• Sec 3π/7 = radians4.494

0

-.3827-1.4281.0515.9004

.7185

Unit Circle

• Fill in the unit circle handout:– Degrees– Radians

• Approximate decimals for quadrantals– π/2 ≈1.57 R , π ≈ 3.14, 3π/2 ≈ 4.71, 2π ≈ 6.28

• We will use this same sheet the rest of the term. Do not lose it. You will not get a new one.

3

1

33

0

3

33

1

u

3

3

33

33

1

1

u

0

tansin,cos

• Notice angles that are multiples of 45° have a 4 in the denominator in radians

• Multiples of 30° have a 6 in the denominator

• Multiples of 60° have a 3 in the denominator

• Approximate decimals for quadrantals– π/2 ≈1.57 R , π ≈ 3.14, 3π/2 ≈ 4.71, 2π ≈ 6.28

• THIS WILL BE IMPORTANT LATER! • We will use this same sheet the rest of the

term. Do not lose it. You will not get a new one.

What quadrant would the following lie in?

• 2.15 R• 5π/8• 1.0 R• 7π/6• 7π/3• 4.97 R

2

2

1

3

1

4

Arc Length and

Area of a Sector

θ MUST BE IN RADIANS!!

Converting from degrees to radians and radians to degrees

• 137° to radian measure

• 5π/11 to degree measure

• 147° to radians to the 4 decimal place

180137

180137

11900180

115

5656.2180

147

The diameter of a circle is 20 cm and the measure of the central angle is 130°.

A. find length of arcB. find area of corresponding sector

• First: write the equations• Second: draw picture and plug values

Third: solve• θ must be in radians to use formulas

Solve:• Must be in radians not degrees. We must

convert:

• Formulas?

• Solve:

s = rθ

1813

180130

2

2rk

1813

10 s2

)1813(102

k

20 cm130º

Angular Velocity

andLinear Velocity

Convert:• Convert 20 rpms to rad/sec

sec32

sec60min1

12

min120

revrev

• Convert 1 revolution in 4 hours to rad/min

min120min601

12

41 hr

revhrsrev

2

• Find the angular velocity of the minute hand of a clock in one minute. Convert to rad/sec

sec1800sec60min1

12

min601

revrev

30

Classwork/Homework

– p. 106 # 7-17 odd, 25-39 odd – p. 113 # 1-9, 11-17 odd, 39-42, 47-48, and

pick one from 22-24– p.55 # 1-7 all, 8-15 all (handout/ problems

for a different book)