61 angles and precalc/trig a radian measure...pre calc/trig a 6 1 angles and radian measure march...
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PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
61
Angles andRadian Measure
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
Radian: a unit of measurement for angles
1 radian = degrees (about 57.3º)
1 degree = radians (about 0.017 radian)
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
Convert from degrees to radians:
1. 115º
2. 240º
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
Unit Circle fill in as many degrees/coordinates as you can remember
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
Now, on the unit circle, use the degree measures to calculate each angle measure in radians
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
Convert from radians to degrees:
1.
2.
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
Remember, that for an angle, , on the unit circle:
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
Evaluate:
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
Central Angle: an angle whose vertex lies at the center of the circle
Circular Arc: a part of a circle, usually defined by the central angle that intercepts it
A
B
is a central angle
is a circular arc
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
Arc Length: the length of any circular arc, s, can be found using the formula
where r = radius of circle
and = radian measure of the central angle
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
Given a central angle of , find the length of its intercepted arc in a circle of radius 15in.
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
Given a central angle of 125º, find the length of its intercepted arc in a circle of radius 7cm.
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
Area of a Sector:
is the angle measured in radians
is the radius of the circle
PreCalc/Trig A
61 Angles and Radian Measure
March 23, 2015
Find the area of a sector if the central angle
measures radians and the radius of the
circle is 11 cm. Round to nearest tenth.