Question

What is $ \dfrac{{15\pi }}{8} $ radians in degrees?

Answer 1

Hint: Convert the given measure of angle radians into the degrees by using the
\[{\text{ Degree = }}\dfrac{{{\text{180}}^\circ }}{\pi } \times {\text{radians}}\]. Place the relation and simplify the equation using the basic mathematical calculations.

Complete step-by-step answer:
We know the basic relation between degrees and radians.
\[{\text{ Degree = }}\dfrac{{{\text{180}}^\circ }}{\pi } \times {\text{radians}}\]
Place the value in the given value –
\[{\text{ Degree = }}\dfrac{{{\text{180}}^\circ }}{\pi } \times \dfrac{{15\pi }}{8}\]
Simplify the above equation, common factors from the numerator and the denominator cancel each other.
\[{\text{ Degree = 337}}^\circ {\text{.5'}}\]
Hence, $ \dfrac{{15\pi }}{8} $ radians is \[{\text{337}}^\circ {\text{.5}}\] in degrees
This is the required solution.
So, the correct answer is “ \[{\text{337}}^\circ {\text{.5}}\] degrees”.

Note: It is very important to know the difference between the system of units and the conversional ratios between them. Since if we say mass of one it does not make any sense, also mass of one gram and one kilogram differs a lot as $ 1kg = 1000g $ .
Always check the units of the given term, all the given terms should be in the same system and then start solving. Also, remember the conversional relations of the different physical quantities and apply accordingly.