What is -pi in degrees?
Answer
589.5k+ views
Hint: A mathematical constant is the number \[\pi \]. It is defined as the circumference to diameter ratio of a circle, with various equivalent definitions.
Complete step-by-step answer:
The angle subtended by an arc of a circle of length equal to the radius is called a radian. If the radius of a circle is $ 1 $ , then a $ 1 $ radian angle determines an arc with a curved length of $ 1.2\pi $ radians would carry us once around the circle.
A degree (full name: degree of arc, arc degree, or arc degree) is a measurement of a plane angle in which one full rotation is 360 degrees. It is typically denoted by $ ^ \circ $ (the degree symbol).
The angle of a full circle is divided into $ 360 $ divisions by degrees. We go around the circle once by turning $ 360 $ degrees.
The formula used to convert radians into degrees, is to multiply the radians by \[{180^ \circ }\,\pi \]radians.
$ 2\pi $ radians equals $ {360^ \circ } $ degrees, while $ \pi $ radians equals $ {180^ \circ } $ .
Hence -pi is $ - {180^ \circ } $ .
So, the correct answer is “ $ - {180^ \circ } $ ”.
Note: Pi is a number that is practically infinite. The number $ 123456 $ , on the other hand, does not appear in the first million digits of pi. It's surprising because if a million digits of pi don't have the sequence $ 123456 $ , it's the rarest number in the world.
Many mathematicians agree that saying a circle has infinite corners is more accurate than saying it has zero. It's only reasonable to assume that the infinite number of corners in a circle corresponds to the infinite number of pi digits.
Complete step-by-step answer:
The angle subtended by an arc of a circle of length equal to the radius is called a radian. If the radius of a circle is $ 1 $ , then a $ 1 $ radian angle determines an arc with a curved length of $ 1.2\pi $ radians would carry us once around the circle.
A degree (full name: degree of arc, arc degree, or arc degree) is a measurement of a plane angle in which one full rotation is 360 degrees. It is typically denoted by $ ^ \circ $ (the degree symbol).
The angle of a full circle is divided into $ 360 $ divisions by degrees. We go around the circle once by turning $ 360 $ degrees.
The formula used to convert radians into degrees, is to multiply the radians by \[{180^ \circ }\,\pi \]radians.
$ 2\pi $ radians equals $ {360^ \circ } $ degrees, while $ \pi $ radians equals $ {180^ \circ } $ .
Hence -pi is $ - {180^ \circ } $ .
So, the correct answer is “ $ - {180^ \circ } $ ”.
Note: Pi is a number that is practically infinite. The number $ 123456 $ , on the other hand, does not appear in the first million digits of pi. It's surprising because if a million digits of pi don't have the sequence $ 123456 $ , it's the rarest number in the world.
Many mathematicians agree that saying a circle has infinite corners is more accurate than saying it has zero. It's only reasonable to assume that the infinite number of corners in a circle corresponds to the infinite number of pi digits.
Recently Updated Pages
Write any three differences between metals and nonmetals class 10 social science CBSE

Amit standing on a horizontal plane finds a bird flying class 10 maths CBSE

Two circles of radii 5 cm and 3 cm intersect at two class 10 maths CBSE

Solve the following i John and Jivanti together have class 10 maths CBSE

What is the relation between orthocenter circumcentre class 10 maths CBSE

Two plane mirrors are inclined at 70circ A ray incident class 10 physics CBSE

Trending doubts
Explain the Treaty of Vienna of 1815 class 10 social science CBSE

Which country is known as "The land of Fire and Ice"?

1 GB equals how many MB?

10 examples of evaporation in daily life with explanations

What is the full form of POSCO class 10 social science CBSE

Make a sketch of the human nerve cell What function class 10 biology CBSE

