What's a radian

Front

What is a radian?

Back

A radian is a unit of angular measure used in mathematics, defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.

Tags

CCSS.HSF.TF.A.1

Front

How many radians are in a full rotation?

Back

There are 2π radians in a full rotation (360 degrees).

Tags

CCSS.HSF.TF.A.1

Front

What is the relationship between degrees and radians?

Back

Degrees and radians are both units for measuring angles. To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π.

Tags

CCSS.HSF.TF.A.1

Front

What are coterminal angles?

Back

Coterminal angles are angles that share the same terminal side when drawn in standard position. They can be found by adding or subtracting multiples of 360 degrees or 2π radians.

Front

What are supplementary angles?

Back

Supplementary angles are two angles whose measures add up to 180 degrees or π radians.

Tags

CCSS.7.G.B.5

Front

What are complementary angles?

Back

Complementary angles are two angles whose measures add up to 90 degrees or π/2 radians.

Tags

CCSS.7.G.B.5

Front

What is the formula for arc length?

Back

Arc length (s) can be calculated using the formula s = rθ, where r is the radius and θ is the angle in radians.

Tags

CCSS.HSG.C.B.5

Front

What is the formula for the area of a sector?

Back

The area of a sector (A) can be calculated using the formula A = (1/2)r²θ, where r is the radius and θ is the angle in radians.

Tags

CCSS.HSG.C.B.5

Front

What is the circumference of a circle?

Back

The circumference (C) of a circle can be calculated using the formula C = 2πr, where r is the radius.

Tags

CCSS.7.G.B.4

Front

What is the relationship between arc length and radius?

Back

The arc length is directly proportional to the radius of the circle; as the radius increases, the arc length increases for the same angle.

Tags

CCSS.HSG.C.B.5