Question

How do you convert $ 345 $ degrees to radians?

Answer 1

Hint: For answering questions of this type we need to apply the concept of conversions of angles from the trigonometric ratios or angles. As the value of one degree is given as $ \dfrac{\pi }{180} $ so the value of $ x $ degrees is given as $ x\times \dfrac{\pi }{180} $ .

Complete step by step answer:
Now considering the question we have been asked to convert $ 345 $ degrees to radians.
For conversion of degrees to radians we need to multiply the given angle with $ \dfrac{\pi }{180} $ because the value of $ \pi $ radians is given as $ {{180}^{{}^\circ }} $ so the value of one degree will be given as $ \dfrac{\pi }{180} $ similarly value of $ x $ degrees is given as $ x\times \dfrac{\pi }{180} $ . This was illustrated to us in the basic concepts of angles or the trigonometric ratios and angles.
This type of conversions helps us while performing further trigonometric simplifications
Therefore the value of $ {{345}^{{}^\circ }} $ is given as $ 345\times \dfrac{\pi }{180} $ .
After performing further simplifications that is by applying the basic algebraic calculations like multiplication and division we will have $ \dfrac{345}{180}\pi =\dfrac{23}{12}\pi $ .
Now after all the calculations and applying the concepts we can come to a further conclusion.
Therefore we can conclude that after all the conversion process $ 345 $ degrees is equal to $ \dfrac{23}{12}\pi $ radians.

Note:
We should be sure with our calculations and concepts that we apply while performing questions of this type. This is a very simple question the chances of mistakes in questions of this type are very less the only possible one is treating the value of $ \pi $ as $ 360 $ degrees which will lead us to a conclusion as the value of $ 345 $ degrees is $ \dfrac{23}{24}\pi $ radians which is clearly a wrong answer.