Question

What is $7\pi$ in degrees?

Answer 1

Hint: We will use the concepts of trigonometry to solve this question. In order to convert $7\pi$ in degrees, we have to use the fact that circumference of a circle is denoted by $2\pi$ and a circle has angle as \[{{360}^{\circ }}\] . So here we have to multiply by \[{{360}^{\circ }}\] and then divide it by $2\pi$.

Complete step-by-step answer:
The question is from the concepts of trigonometry. A radian can be defined as the number of segments whose length is equal to the radius of the circle. The circumference of the circle upon the length of the radius of the circle is the measurement of a radian.
The Circumference (C) of a circle which has a radius r is denoted by \[2\pi \] multiplied by r.
\[\Rightarrow \] Circumference = \[2\pi \cdot r\]
\[\Rightarrow \]Radian = \[\dfrac{C}{r}\]
\[\Rightarrow \]Radian = \[2\pi \]
A circle has a total of \[{{360}^{\circ }}\]. So, relating these two we get,
\[\Rightarrow \] \[2\pi \](Radians) = \[{{360}^{\circ }}\]
\[\Rightarrow \]\[\pi \](Radians) = \[{{180}^{\circ }}\]
So, from the above equations we can clearly say that 1 radian = \[{{\left( \dfrac{180}{\pi } \right)}^{\circ }}\]
Given, \[7\pi \], So converting to degrees, we get
\[\Rightarrow \] \[7\pi \] (Radians) = \[7\pi \times {{\left( \dfrac{180}{\pi } \right)}^{\circ }}\]
\[\Rightarrow \] \[7\pi \] (Radians) = \[{{1260}^{\circ }}\]
\[\therefore \] \[7\pi \] is equal to \[{{1260}^{\circ }}\].

Note: When we are given such a value like \[7\pi \], we have to first define and clearly understand the value between radians and degrees. This would help us clearly understand the conversion between the two and arrive at the right answer. There is commonly a confusion between degrees and radians. Also, a thing to remember is that a circle in total has \[{{360}^{\circ }}\]i.e., \[2\pi \]. Also, the circumference of the circle with radius \[r\] and diameter \[d\] is given as \[2\pi \cdot r\] or also \[\pi \cdot d\] since \[d=2r\]. If we are given any measurement in radian, we can find the measurement in degrees respectively just by converting them from degrees to radian and vice versa as required.