Why is Calculus Important? Skills are Interchangeable But just because they don’t use it in a direct way, that doesn’t imply that it’s not worth studying. Ironically, many physicist and scientists don’t use calculus after their college graduation. Should you really take classes in calculus, algebra, trigonometry, and all the other stuff that the majority of people are never going to use in their lives again? But calculus, that scary monster that haunts many high-schoolers’ dreams, how crucial is that?

According to experts, doing so should be in anyone’s “essential skills” checklist.Ĭounting is crucial, and so are multiplying and percentages. Learning mathematics is definitely one of the most important things to do in life. The major arc is the arc that connects the two points with a central angle greater than 180°, while the minor arc is the arc that connects the two points with a central angle less than 180°.Calculus Calculator: Learn Limits Without a Limit! When two points on a circle divide the circumference into two arcs, the major arc is the larger arc, and the minor arc is the smaller arc. Try our area calculator to calculate the area of a sector and several other shapes. The area of a sector A is equal to the radius r squared times the central angle θ, divided by 2. The area of a sector can be found using the formula: Thus, the length of the chord a is equal to 2 times the radius r times the sine of the central angle θ divided by 2. The length of the chord can be found using the following formula: The chord length will always be shorter than the arc length, since the chord is the straight-line distance between the two points, while the arc is the curved distance between them. The chord, represented as line a in the sector image above, is the line that connects the points where the radii intersect the arc. The arc length s is equal to the square root of 2 times the central angle θ in radians, times the sector’s area A divided by θ.Ī sector is divided by the chord into a triangle and an outer segment. You can also find the length of the arc if the sector area and central angle are known using the formula: Using the radius and the central angle, you can use the formula above to find the length of the arc.įind Arc Length using Sector Area and Central Angle The radius r of a sector is equal to the chord length a divided by the quantity 2 times the sine of the central angle θ divided by 2. If you know the central angle and chord length, but you don’t know the radius, then you need to find the radius before you can use the arc length formula.īy solving the above formula for the radius, you can find the radius of a sector with the formula: Now, you can use the central angle and radius to find the arc length using the formula above.įind Arc Length using the Central Angle and Chord Length

If using units, the chord length and the radius must have the same units. The central angle θ in radians is equal to 2 times the inverse sine function of the chord length a divided by 2 times the sector radius r. Given this information, you can find the central angle of a sector with the formula: If you know the radius and chord length, but you don’t know the central angle, then you need to find the central angle first in order to use the formula above. Thus, the arc length s is equal to 14 meters.įind Arc Length using the Radius and Chord Length In addition, if you don’t know the radius of the circle, but you do know its diameter, then you can find the radius by dividing the diameter by two.įor example, let’s find the arc length of a sector with a radius of 7 meters and a central angle of 2 radians.Īrc length (s) = 7 m × 2 rad arc length (s) = 14 m You can also use our degrees to radians converter to convert degrees to radians. If you have an angle measured in degrees, you can convert it to radians by multiplying the angle by π divided by 180. Radians are considered unitless, so by using radians for the angle, the units will be correct. Note that the central angle must be in radians, not degrees, because the units must be the same on both sides of the equation.Īrc length has units of distance, as does radius, so if the central angle were in degrees, we would have distance = degree-distance which does not make sense. Thus, the length of an arc is equal to the radius r of the sector times the central angle in radians. You can find the length of the sector’s arc using an easy formula.įor a given radius r and central angle θ, the following formula defines the arc length s of a sector. Semicircles, quadrants, and slices of pizza or pie are just some examples of sectors.

Arc length calculus calculator