Question

What is 450 degrees in terms of radians?

Answer 1

We are given with an angle in degrees which we have to express in radians We know that,${{180}^{\circ }}=\pi radians$ as $2\pi$ would mean a complete circle which is ${{360}^{\circ }}$. So, ${{1}^{\circ }}=\dfrac{\pi }{{{180}^{\circ }}}radians$ we multiply the given angle in degrees by $\dfrac{\pi }{{{180}^{\circ }}}$ to express the angle in radians. Reducing it further, cancelling the common terms, we will have the angle in radians.

Complete step by step solution:
According to the given question we have been given an angle which Expressed in degrees, that is, we have 450 degrees. We have to now express this angle in radians.
We will begin with writing the given angle in degrees we have,
$\Rightarrow {{450}^{\circ }}$
We know that a complete circle measures ${{360}^{\circ }}$ which in radians terms would be $2\pi$. So, far a half circle that is ${{180}^{\circ }}$ has the angle in radian terms as $\pi radians$.
We can now write it as
$\Rightarrow {{360}^{\circ }}=2\pi radians$
$\Rightarrow {{180}^{\circ }}=\pi radians$
So, for 1 degree we have
$\Rightarrow {{1}^{\circ }}=\dfrac{\pi }{{{180}^{\circ }}}radians$
We will use this conversion factor to get the angle of the required unit, that is we will multiply the given angle in degrees by $\dfrac{\pi }{{{180}^{\circ }}}$ and further solving which gives us the angle radians
We have
If ${{1}^{\circ }}=\dfrac{\pi }{{{180}^{\circ }}}radians$
Then for 450 degrees
$\Rightarrow {{450}^{\circ }}=\dfrac{\pi }{{{180}^{\circ }}}\times {{450}^{\circ }}radians$
We will now solve $\dfrac{\pi }{{{180}^{\circ }}}\times {{450}^{\circ }}radians$ and we get,
$\Rightarrow \dfrac{\pi }{{{180}^{\circ }}}\times {{450}^{\circ }}radians$
By solving further, we will get,
$\Rightarrow \dfrac{\pi }{2}\times 5radians$
$\Rightarrow \dfrac{5\pi }{2}radians$
Therefore, the 450 degrees in radians is $\dfrac{5\pi }{2}radians$

Note: The conversion factor for degrees to radians is ${{1}^{\circ }}=\dfrac{\pi }{{{180}^{\circ }}}radians$
Similarly, the conversion factor for radians to degree is $1radian=\dfrac{{{180}^{\circ }}}{\pi }degree$
The conversion factor should be carefully written and calculation should be cone in a proper sequence to avoid errors .