What is the radian measure of a circle?

symbol rad. The radian measure of a central angle θ of a circle is defined as the ratio of the length of the arc the angle subtends, s, divided by the radius of the circle, r. Note that when s = r, we get θ expressed as one radian.

What is a circular measure used?

A circular measure was used in comparing circular cross-sections, e.g., of wires, etc. A circular unit of the ares is the area of the circle whose diameter is one linear unit. For example, 1 circular mil is equivalent to 0.7854 square mil in area, 1 circular millimeter = 1550 circular mils = 0.7854 square millimeter.

What is the radian measure of 75?

5π12
Hence, the value of 75∘ in radians is 5π12.

Why do we use radian measure?

Radians make it possible to relate a linear measure and an angle measure. The length of the arc subtended by the central angle becomes the radian measure of the angle. This keeps all the important numbers like the sine and cosine of the central angle, on the same scale.

How do you find a circular measure?

The length of an arc of a circle is given by s=r⋅θ s = r ⋅ θ , where r is the radius and θ is the angle subtended in radians.

What is radian class 9?

Answer: 1 radian is the angle which an arc of length equal to the radius of a circle subtends at the centre of the circle. The arc of a circle subtends an angle at the centre of the circle. Its unit is radian.

What is 5pi 12 on the unit circle?

0.9659
The value of sin 5pi/12 can be calculated by constructing an angle of 5π/12 radians with the x-axis, and then finding the coordinates of the corresponding point (0.2588, 0.9659) on the unit circle. The value of sin 5pi/12 is equal to the y-coordinate (0.9659). ∴ sin 5pi/12 = 0.9659.

How many radians is 240?

2400=3π2.

What is the measure of 1 radian in a circle?

Angle subtended at the centre by an arc of length 1 unit in a unit circle (circle of radius 1 unit) is said to have a measure of 1 radian. The symbol used to denote the radian measure is “ rad ” or “ c ”. This is shown in the figure given below.

What is the symbol used to denote the radian measure?

The symbol used to denote the radian measure is “ rad ” or “ c ”. This is shown in the figure given below. The circumference of a circle of radius 1 unit is 2π since the circle’s circumference with radius “r” is 2πr. Thus, one complete revolution of the initial side subtends an angle of 2π radians.

How many radians does the circumference of a circle subtend?

An arc of a circle with the same length as the radius of that circle subtends an angle of 1 radian. The circumference subtends an angle of 2π radians.

What is the circumference of a circle of radius 1?

The circumference of a circle of radius 1 unit is 2π since the circle’s circumference with radius “r” is 2πr. Thus, one complete revolution of the initial side subtends an angle of 2π radians. Further, in a circle of radius r, an arc of length r will subtend an angle of 1 radian. Also, learn more about Arc here.