Question

How do you express $45$ degrees in radian in terms of pi?

Answer 1

In this question, we have to find out the required from the given particulars.
We need to express the angle given in radian in terms of pi. For that we first need to know the relation between degree and radian and apply that formula by putting the given angle in degree. After solving the result we can find out the required solution.

Formula used:
$1$ Degree $= \dfrac{\pi }{{180}}$ radian

Complete step by step answer:
The given angle is $45$ degree.
We need to express it in radian in terms of pi.
We know, $1$ Degree $= \dfrac{\pi }{{180}}$radian
Now applying the formula and by unitary method we can write the angle in radian terms of pi.
Hence, $45$ degree $= \dfrac{\pi }{{180}} \times 45$ Radian
Solving that we get, $45$ degree $= \dfrac{\pi }{4}$ Radian

Hence, expressing $45$degrees in radian in terms of pi, we get, $45$ degree $= \dfrac{\pi }{4}$ Radian.

Note: A degree usually denoted by $^\circ$(the degree symbol) is a measurement of a plane angle in which one full rotation is $360$ degrees.
It is not an SI unit —the SI unit of angular measure is the radian —but it is mentioned in the SI brochure as an accepted unit because a full rotation equals $2\pi$radians, one degree is equivalent to $\dfrac{\pi }{{180}}$ radians.
Relation between degree, radian and grade is
$\dfrac{{Degree}}{{90}} = \dfrac{{Grade}}{{100}} = \dfrac{{2Radian}}{\pi }$
In most mathematical work beyond practical geometry, angles are typically measured in radians rather than degrees. This is for a variety of reasons; for example, the trigonometric functions have simpler and more "natural" properties when their arguments are expressed in radians. These considerations outweigh the convenient divisibility of the number $360$.