Question

How do you convert \[105\] degrees to radians?

Answer 1

Hint: These types of problems are pretty straight forward and are very simple to use. First of all we need to know the general form of how an angle is represented and how we can convert this angle to any other forms. Generally angles are mainly represented in two forms, they are degrees and radians, and both of them are interconvertible, which means, we can convert from radian to degrees and vice-versa. The relation between converting from degrees to radians is, one hundred and eighty degrees is equal to pi radians, and using this relation formula we can very easily convert from one form to another very smoothly.

Complete step by step solution:
Now, we start off with the solution to the given problem by writing that, the relation between degree and radian is,
\[{{180}^{\circ }}=\pi \] radians.
Now, we just apply the linear theory of equations to find the value of \[105\] degrees in radians.
We can therefore write that,
\[{{1}^{\circ }}=\dfrac{\pi }{180}\] radians.
Now, to find the radians for \[105\] degrees we just multiply \[105\] on both the sides of the equation, and by doing this we get,
\[{{105}^{\circ }}=\dfrac{\pi }{180}\times 105\]
Now dividing the numerator and the denominator of the right hand side of the equation by \[15\] , we get,
\[{{105}^{\circ }}=\dfrac{7\pi }{12}\]
Thus we can say that the value of \[105\] degrees is equivalent to \[\dfrac{7\pi }{12}\] radians.

Note: For such problems, we need to have the knowledge of how many ways we can represent the angles. We also must be fully aware of the relation that holds well in converting one form of the angle to another. These things help us in solving the problems more efficiently and effectively. In trigonometry we generally use the radian form of the angles, so an interconversion form degree to radian becomes necessary.