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If the arc length of a sector in the unit circle is 4.2 what is the measure of the angle of the sector?
In a unit circle, the radius is 1, so the arc length ( s ) of a sector can be calculated using the formula ( s = r\theta ), where ( r ) is the radius and ( \theta ) is the angle in radians. Since the radius ( r = 1 ), the formula simplifies to ( s = \theta ). Therefore, if the arc length is 4.2, the measure of the angle of the sector is ( \theta = 4.2 ) radians.
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If the arc length of a sector in the unit circle is 3 radians what is the measure of the angle of the sector?
In a unit circle, the arc length ( s ) is directly equal to the angle ( \theta ) in radians. Therefore, if the arc length of a sector is 3 radians, the measure of the angle of the sector is also 3 radians.
What is the name of the angle in a circle sector?
The angle in a circle sector is called the "central angle." This angle is formed at the center of the circle and subtends the arc of the sector. It is measured in degrees or radians and determines the size of the sector.
How can you find the measure of the central angle with the sector area known?
It is found by: (sector area/entire circle area) times 360 in degrees
How can the radian measure of an angle determine the arc length on the unit circle?
The radian measure IS the arc length of the unit circle, by definition - that is how the radian is defined in the first place.
How do you work out the area of a sector when given the length of the arc?
If you're only given the length of the arc, then you can't. You also need to know the fraction of the circle that's in the sector. You can figure that out if you know the angle of the arc, or the radius or diameter of the circle. -- Diameter of the circle = 2 x (radius of the circle) -- Circumference of the circle = (pi) x (Diameter of the circle) -- (length of the arc)/(circumference of the circle) = the fraction of the whole circle that's in the sector or -- (degrees in the arc)/360 = the fraction of the whole circle that's in the sector -- Area of the circle = (pi) x (radius of the circle)2 -- Area of the sector = (Area of the circle) x (fraction of the whole circle that's in the sector)
If the arc length of a sector in the unit circle is 3 radians what is the measure of the angle of the sector?
In a unit circle, the arc length ( s ) is directly equal to the angle ( \theta ) in radians. Therefore, if the arc length of a sector is 3 radians, the measure of the angle of the sector is also 3 radians.
To find the area of a sector you multiply the area of the circle by the measure of the arc determined by the sector?
Area of sector/Area of circle = Angle of sector/360o Area of sector = (Area of circle*Angle of sector)/360o
What is the relation between area of a sector and length of an arc of a circle?
There is no direct relation between the area of a sector and the length of an arc. You must know the radius (or diameter) or the angle of the sector at the centre.
If the ratio of a circle's sector to its total area is 78 what is the measure of its sector's arc?
Length of arc = angle of arc (in radians) × radius of circle With a ratio of 7:8 the area of the sector is 7/8 the area of the whole circle. This is the same as saying that the circle has been divided up into 8 equal sectors and 7 have been shaded in. Dividing the circle up into 8 equal sectors will give each sector an angle of arc of 2π × 1/8 7 of these sectors will thus encompass an angle of arc of 2π × 1/8 × 7 = 2π × 7/8 = 7π/4 Thus the length of the arc of the sector is 7π/4 × radius of the circle. --------------------------------- Alternatively, it can be considered that as 7/8 of the area is in the sector, the length of the arc is 7/8 the circumference of the circle = 7/8 × 2π × radius = 7π/4 × radius.
A circle has a radius of 6.5 inches. The area of a sector of this circle is 75 in2. Approximate the measure of the central angle, in radians, of this sector, rounded to the nearest tenth?
6.5
If the arc on a particular circle has an arc length of 12 inches and the circumference of the circle is 48 inches what is the angle measure of the arc?
The angle measure is: 90.01 degrees
How can you find the measure of the central angle with the sector area known?
It is found by: (sector area/entire circle area) times 360 in degrees
How do you find radius using angle of a sector?
It depends on what else is known about the sector: length of arc, area or some other measure.
How can the radian measure of an angle determine the arc length on the unit circle?
The radian measure IS the arc length of the unit circle, by definition - that is how the radian is defined in the first place.
How do you work out the area of a sector when given the length of the arc?
If you're only given the length of the arc, then you can't. You also need to know the fraction of the circle that's in the sector. You can figure that out if you know the angle of the arc, or the radius or diameter of the circle. -- Diameter of the circle = 2 x (radius of the circle) -- Circumference of the circle = (pi) x (Diameter of the circle) -- (length of the arc)/(circumference of the circle) = the fraction of the whole circle that's in the sector or -- (degrees in the arc)/360 = the fraction of the whole circle that's in the sector -- Area of the circle = (pi) x (radius of the circle)2 -- Area of the sector = (Area of the circle) x (fraction of the whole circle that's in the sector)
How can you find the angle of a sector in a circle?
Multiply ( pi R2 ) by [ (angle included in the sector) / 360 ].
How do you find the degree measure of a central angle in a circle if both the radius and the length of the intercepted arc are known?
-- Circumference of the circle = (pi) x (radius) -- length of the intercepted arc/circumference = degree measure of the central angle/360 degrees
