Question

How do you convert 17 degrees into radians?

Answer 1

Hint: We will note that ${180^ \circ } = \pi $, then we will find out the equivalence of 1 degrees in terms of pi and thus by multiplying it by 17, we have the required answer.

Complete step by step solution:
We are given that we need to convert 17 degrees into radians.
Since, we know that we have the following expression with us:-
$ \Rightarrow \pi = {180^ \circ }$
This means that we have 180 degrees in radians as follows:-
$ \Rightarrow {180^ \circ } = \pi $ radians
Now, we will use a unitary method to find out above 1 degree.
Thus, we will have the following equation with us:-
$ \Rightarrow {1^ \circ } = \dfrac{\pi }{{180}}$ radians
Now, let us multiply both the sides of the above equation by 17, we will then obtain the following expression with us:-
$ \Rightarrow {1^ \circ } \times 17 = 17 \times \dfrac{\pi }{{180}}$ radians
Simplifying the calculations on both the sides of the above equation, we will then obtain the following equation with us:-
$ \Rightarrow {17^ \circ } = \dfrac{{17\pi }}{{180}}$ radians

Note: The students must note that we have made use of a single fact in the whole solution mentioned above that is given by the following expression:-
$ \Rightarrow \pi = {180^ \circ }$
The students must also note that we cannot simplify the final answer further because 17 is a prime number and it cannot have any common factor with 180 and thus we cannot cancel out any of the factors. {In other words: Basically HCF (17, 180) = 1, therefore, none of the factors can be crossed off from both)
The students must also know the facts about degree and radians given by the following points:-
1. The radian measure is purely based on the measurement of radius, therefore, it is known as radians.
2. To go from radians to degrees: multiply by 180, divide by $\pi $ .To go from degrees to radians: multiply by $\pi $, divide by 180.