Question

How do you change 1400 to radian measure in terms of pi?

Answer 1

Hint: This question is from the topic of trigonometry. In this question, we will convert 1400 degrees to radian. In solving this question, we will first understand about degrees and radians from a circle. After that, we will solve for 1400 degrees and find that value in the form of radian containing pi in that term. After solving the further question, we will get our answer.

Complete step by step answer:
Let us solve this question.
In this question, we have asked to change 1400 degree to radian. It is given in the question that we will convert the term so that there will be pi or \[\pi \].
So, let us understand from a circle.
A circle has 360 degrees or we can write \[360{}^\circ \].
A circle also consists 2pi or \[2\pi \] radians.
So, we can say that both will be equal. we can write them as
\[2\pi =360{}^\circ \]
So, we get that in \[360{}^\circ \], it is \[2\pi \] radians.
Similarly, we can say that in \[1{}^\circ \], it will be \[\dfrac{2\pi }{360}\] radians.
Similarly, we can say that in 1400 degrees or \[1400{}^\circ \], it will be \[\dfrac{2\pi }{360}\times 1400\] radians.
We can write the term \[\dfrac{2\pi }{360}\times 1400\] as
\[\dfrac{2800\pi }{360}\]
The above can also be written as
\[\Rightarrow \dfrac{280\pi }{36}=\dfrac{70\pi }{9}\]
If we divide 70 by 9, then we will get as 7.77777
Hence, we can write the above equation as
\[\Rightarrow \dfrac{280\pi }{36}=7.77777\pi \]
This term is containing pi that is \[\pi \] also.

So, we can say that the conversion of \[1400{}^\circ \] in radian measure in terms of pi (or \[\pi \]) is \[7.77777\pi \].

Note: We should have a better knowledge in the topic of trigonometry to solve this type of question easily. We should know that in a circle, it is \[360{}^\circ \] (or 360 degrees). Similarly, we can see that in a circle it is \[2\pi \] (or 2pi) radians. So, always remember that \[2\pi \] is always equal to 360 degrees. Or, we can write this in mathematical form as \[2\pi =360{}^\circ \].