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Why does the formula for area of a sector one half r-squared theta not hold true if theta is measured in degrees?
If this is a homework assignment, please consider trying it yourself first, otherwise the value of the reinforcement to the lesson offered by the homework will be lost on you.
The area of a circle is pi r2.
The area of a sector, defined as the proportion of an angle theta over the angle of a full circle is (pi r2 theta) / (2 pi). That simplifies to (r2 theta) / 2.
Using degrees, the same equation is (pi r2 theta) / 360. That does not simplify any further.
The reason for this is that theta in radians is defined as the proportion of the circumference of the circle, which is 2 pi r. This makes the math come out easier, which is why most trigonometry is done in radians, not degrees.
What else can I help you with?
What is the formula of the sector of the circle?
There is no specific formula for a sector of a circle. There is a formula for its angle (at the centre), its perimeter, its area.
How do you find the area of a shaded sector of a sector?
The area is r^2*x where r is the radius of the circle and x is the angle measured in radians. If you are still working in degrees then Area = (y/180)*r^2, where the angle is y.
Find the area of the sector when the sector measures 10 degrees and the diameter of the circle is 12?
For a circle where sector measures 10 degrees and the diameter of the circle is 12: Sector area = 3.142 square units.
How do you find the area of a segment of a circle?
In order to find the area of a sector of a circle you can use the formula below: pi*r^2 * # of degrees/ 360
Find the sector area of a sector with radius of 30 and an angle of 60 degrees?
apply this formula: A = t/360 r2 when t = angle at center and r = radius so A = 471.2 (rounded to 1 decimal place)
What is the radius of the sector with an angle of 27 degrees and arc of 12cm?
The radius of the sector with an angle of 27 degrees and arc of 12cm is: 25.46 cm
How do you find the sector area of a circle?
The area of a sector is 0.5*r^2*theta square units where r is the radius measured in linear units and theta is the angle (measured in radians).
What is the largest sector of the macroeconomy?
The largest sector of the macroeconomy is the consumer sector. Macroeconomic output is typically measured by GDP, which stands for Gross Domestic Product.
What is the area of the sector of a circle?
Suppose the radius of the circle is r units and the sector subtends an agle of x radians at the centre of the circle. ThenArea = 0.5*r2*x square units.If x is measured in degrees, this becomesArea = pi*r2*x/360 square units.
How do you find the degrees sector of an circle?
It depends on what information you have: the radius and the area of the sector or the length of the arc.
Calculate a sector of a circle if the angle is 150 degrees and the radius is 13cm?
The area of the sector is: 221.2 cm2
What is the degree measure of 11 percent sector?
The angle of the sector measures 39.6 degrees (.11*360).
