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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)
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