Question

What is the difference between degrees and radians on the calculator and why do they affect the answers?

Answer 1

Hint: Questions like these are quite easy to understand and simple to solve once we understand the underlying concepts behind the problem. To solve this problem effectively we need to have a firm grasp on topics like trigonometric angles and values and conversion from radians to degrees and vice versa. First of all we need to understand what degrees and radians mean and how are they connected or related to one another. After that we will see how using one instead of the other will affect our answers and may lead to a wrong solution.

Complete step-by-step solution:
Now we start off with the solution to the given problem by writing that a degree is defined as the unit angle which a line makes with the x-axis in a two dimensional plane. In other words we can also say that a degree is one which is formed when a full circle is divided into \[360\] equal parts. On the other hand we say that a radian is the angle that is subtended by an arc of length equal to the radius of the circle at the centre of the circle. Radian and degree are related to one another as,
\[{{180}^{\circ }}={{\pi }^{c}}\] , or we say, \[180\] degrees is equal to \[\pi \] radians. So if we are using degrees instead of radians or vice-versa, we need to be careful in converting to the required form using the given relation.

Note: Problems like these require a thorough knowledge of geometry and trigonometric equations and values. We need to be very careful while using degrees and radians and if required can convert one form to the other using the relation \[{{180}^{\circ }}={{\pi }^{c}}\] . If we use one in place of another, it will cause an error which finally leads to a wrong solution to the problem. We can easily change the modes from radian to degrees or vice-versa on our calculator by simply pressing a button.