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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.
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