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In the diagram and ampangleABC 90 and deg. What is the radius of the circle?
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∙ 6y ago
I can see no diagram.
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∙ 6y ago
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What is 105 degrees on a radian unit circle?
105 deg = 1.8326 radians approx. The radius of the circle has no effect on the measurement of angles.
What is the radius of a circle with a degree of 240 and sector area of 10?
240 deg gives a sector area of 10 sq units so 360 deg would give a sector area of 10*360/240 = 15 sq units ie the area of the whole circle is 15 sq units or π*r2 = 15 so that r = 2.1851 units (to 4 dp)
How do you translate radian measure into measurements?
When you work with triangles you are using degrees to measure its angles, but when you are working with circles is more convenient to use the radian measure.What is a radian?Definition: A radian is the measure of an angle that, when drawn as a central angle of a circle, intercepts an arc whose length is equal to the length of a radius of the circle.For example,1. When a central angle of a circle with a radius 1cm intercepts an arc of the circle which is also 1cm, this angle has 1 radian measure.2. If you'll make this central angle bigger in order to intercept an arc of the circle whose length will be 2cm (or 2 radius length long), this bigger angle has a measure of 2 radians.3. If you'll make the second central angle of the circle bigger in order to intercept an arc whose length will be 3cm (or 3 radius length long), this angle has a measure of 3 radians.These three cases illustrate the following relationship:measure of an angle in radians = length of the intercepted arc/length of the radiusSo, if you label the angle with x, the length of the intercepted arc with s, and the length of the radius with r, you find the general formula: x = s/rIf you look at the picture of this circle you will see that in a half of the circle you can find a little more than 3 radians, and you need to go a little more far to make a full half of the circle. So, what is the number of radians that you need to go in order to make a full half of the circle?Let's look at this.Let's make a circle. If AB is a diameter of circle O with radius of length r, the points A and B separate the circle into two semicircles. Let's label the angle AOB with x, and the semicircle length with s.You will see that the angle AOB is a central angle of the circle, so the measure of this angle in radians is equal to the length of the intercepted arc AB, which is s, divided by the length of the radius which is r. (See the general formula above)You know that the circumference of the circle is:C = 2(pi)r, since s = C/2 we write:s = [2(pi)r]/2s = (pi)r, substitute this at the general formulax = s/rx = [(pi)r]/rx = piSince x is in radians we can say that in a half of the circle there is pi radians.But we know at the same time that in a half of circle there is 180 degrees, so we can say that the following relationship is true.180 deg = pi radNow you can see why is convenient to work with radians in a circle, because there is exactly pi radians in a half of the circle, and from this relationship we can see how radians are relating to degree measures.Now for a full circle how many degrees are?There are 360 degrees. How many radians it that will be?180 deg = pi rad360 deg = 2pi radSo there are 2pi rad in a full of a circle.Now you start to see why the circumference of a circle is 2(pi)r. Because we know that there are 2pi radius length arcs on a circle.How to convert degrees to radians?We know that:180 deg = pi rad Let's write this a little bit differently180(1 deg) = pi rad1 deg = (pi/180) rad So, what about 5 degrees? Just multiply both sides by 55(1 deg) = 5(pi/180) rad What about x deg?So, let' go t the general formula:x(1 deg) = x(pi/180) radso you have the general formula to use it when you need to convert degrees to radiansHow to convert radians to degrees? pi rad = 180 deg pi(1 rad) = 180 deg 1 rad = 180/pi deg What about 5 radians? Just multiply both sides by 5 5(1 rad) = 5(180/pi) deg What about x radians? So let's go to the general formula: x(1 rad) = x(180/pi) degSo you have the general formula to use it when you need to convert radians to degrees.
How do you get the radius if angle is 150 degrees and length of arc is 330 cm?
150 deg is 150/360 of a complete circle circumference, so the arc length 330cm = 150/360 times 2pi.R This can be solved for R to get R = 330x360/150/(2pi).
If a central angle measures 87 and deg then its arc will measure .?
The same as the central angle of the circle
What is 105 degrees on a radian unit circle?
105 deg = 1.8326 radians approx. The radius of the circle has no effect on the measurement of angles.
What is the length of the arc on a circle with radius 10 cm intercepted by a 20 and deg angle Use 3.14 for and pi .?
The arcs are 59.31 cm and 3.49 cm.
If an arc length of 106 ft is traced by a rotation of 225 deg what is the radius of the circle?
Circumference = 106 x 360/225 = 169.6 ft = 2 x pi x radius so radius = 84.8/pi = 27 feet as near as makes no difference
If a circle of radius 18.1 mm rotates through an angle of 68 deg what is the length of the arc created?
(2 pi) x (18.1) x (68/360) = 21.5 mm (rounded)
A formula for a circle?
In the coordinate plane: (x - a)2 + (y - b)2 = r2 where the centre of the circle is at (a, b) and the radius is r. In parametric form, it is x = a + r*cosΦ y = b + r*sinΦ where 0 ≤ Φ < 360 deg.
What is the radius of a circle with a degree of 240 and sector area of 10?
240 deg gives a sector area of 10 sq units so 360 deg would give a sector area of 10*360/240 = 15 sq units ie the area of the whole circle is 15 sq units or π*r2 = 15 so that r = 2.1851 units (to 4 dp)
What is the area of the shaded sector if the circle has a radius of 4 and the central angle is 90 degrees?
An entire circle is 360 degrees. 90 deg is 1/4 of that. Area of a circle is A = pi r^2 area of this sector is (1/4) pi r^2 = (1/4) x 3.14 x 4x4 =12.56
How do you translate radian measure into measurements?
When you work with triangles you are using degrees to measure its angles, but when you are working with circles is more convenient to use the radian measure.What is a radian?Definition: A radian is the measure of an angle that, when drawn as a central angle of a circle, intercepts an arc whose length is equal to the length of a radius of the circle.For example,1. When a central angle of a circle with a radius 1cm intercepts an arc of the circle which is also 1cm, this angle has 1 radian measure.2. If you'll make this central angle bigger in order to intercept an arc of the circle whose length will be 2cm (or 2 radius length long), this bigger angle has a measure of 2 radians.3. If you'll make the second central angle of the circle bigger in order to intercept an arc whose length will be 3cm (or 3 radius length long), this angle has a measure of 3 radians.These three cases illustrate the following relationship:measure of an angle in radians = length of the intercepted arc/length of the radiusSo, if you label the angle with x, the length of the intercepted arc with s, and the length of the radius with r, you find the general formula: x = s/rIf you look at the picture of this circle you will see that in a half of the circle you can find a little more than 3 radians, and you need to go a little more far to make a full half of the circle. So, what is the number of radians that you need to go in order to make a full half of the circle?Let's look at this.Let's make a circle. If AB is a diameter of circle O with radius of length r, the points A and B separate the circle into two semicircles. Let's label the angle AOB with x, and the semicircle length with s.You will see that the angle AOB is a central angle of the circle, so the measure of this angle in radians is equal to the length of the intercepted arc AB, which is s, divided by the length of the radius which is r. (See the general formula above)You know that the circumference of the circle is:C = 2(pi)r, since s = C/2 we write:s = [2(pi)r]/2s = (pi)r, substitute this at the general formulax = s/rx = [(pi)r]/rx = piSince x is in radians we can say that in a half of the circle there is pi radians.But we know at the same time that in a half of circle there is 180 degrees, so we can say that the following relationship is true.180 deg = pi radNow you can see why is convenient to work with radians in a circle, because there is exactly pi radians in a half of the circle, and from this relationship we can see how radians are relating to degree measures.Now for a full circle how many degrees are?There are 360 degrees. How many radians it that will be?180 deg = pi rad360 deg = 2pi radSo there are 2pi rad in a full of a circle.Now you start to see why the circumference of a circle is 2(pi)r. Because we know that there are 2pi radius length arcs on a circle.How to convert degrees to radians?We know that:180 deg = pi rad Let's write this a little bit differently180(1 deg) = pi rad1 deg = (pi/180) rad So, what about 5 degrees? Just multiply both sides by 55(1 deg) = 5(pi/180) rad What about x deg?So, let' go t the general formula:x(1 deg) = x(pi/180) radso you have the general formula to use it when you need to convert degrees to radiansHow to convert radians to degrees? pi rad = 180 deg pi(1 rad) = 180 deg 1 rad = 180/pi deg What about 5 radians? Just multiply both sides by 5 5(1 rad) = 5(180/pi) deg What about x radians? So let's go to the general formula: x(1 rad) = x(180/pi) degSo you have the general formula to use it when you need to convert radians to degrees.
How do you get the radius if angle is 150 degrees and length of arc is 330 cm?
150 deg is 150/360 of a complete circle circumference, so the arc length 330cm = 150/360 times 2pi.R This can be solved for R to get R = 330x360/150/(2pi).
If a central angle measures 87 and deg then its arc will measure .?
The same as the central angle of the circle
Why are the sun rays never vertical on the Arctic Circle?
Because the Earth's axis is tilted by 23.5 degrees, it only allows the sun to be overhead at some time of the year in locations between the Tropic of Cancer (23.5 deg N) and the Tropic of Capricorn (23.5 deg S). The Arctic Circle is at 66.5 deg N, so the sun is never directly overhead at any time of the year.
Is it possible to divide a circle into 22 parts?
Yes, each pie shaped piece will be 16.3636363636 deg
