Question

How do you convert $ - 70$ degrees into a radian measure?

Answer 1

Hint: Let us first understand the degree. A degree, abbreviated as\[^\circ \], is a unit of measurement for a plane angle with a complete rotation of \[360\] degrees. Although it is not a SI unit (the radian is the SI unit of angular measure), it is mentioned as an agreed unit in the SI brochure.

Complete step by step answer:
The majority of you are used to thinking of a circle in terms of degrees: \[360^\circ \]represents the entire circle. Half of a circle is \[180\] degrees, and so on. Radian measurement is simply another way of expressing the circle. Radian measurement is just a different measurement unit.

We can measure a circle in degrees (as in the old days) or radians (welcome to the major leagues!) just as we can measure a football field in yards or feet. Consider the tone of the word radian: it's similar to the word 'radius.' It turns out that a radian and a circle's radius have a similar relationship.

A radian is the length of an arc that intersects an arc whose length is equal to the radius of the circle when drawn as a central angle of a circle. The general formula for converting degrees to radians is to multiply the number of degrees by $\dfrac{\pi }{{{{180}^ \circ }}}$.
$\therefore \, - 70 \times \dfrac{\pi }{{180}} = - 0.388\pi \,rad = - 1.22\,rad$

Note: To solve such question we should keep all the points in mind. Now let us think about if we go the reverse way. To convert radians to degrees, there is a simple formula.$1\pi $ radian equals \[180\] degrees. As a result, converting from one unit of measure to another is easy.