Question

How do you convert 105 degrees to radians?

Answer 1

Hint: Both degree and radian are two units of measure for an angle. One is called degree (denoted by \[{}^\circ \] sign). And, the other unit of measure is radian, radian is denoted by rad. To solve the given problem, we should know the conversion formula for the degrees to the radian system. The conversion formula states that measure in radian = measure of angle in degree \[\times \dfrac{\pi }{180{}^\circ }\]. As the above measure in the degree system is negative, the radian system measure will also be negative.

Complete step by step solution:
We are given the measure of angle in degrees is \[-105\], we need to convert it to the radian system. We know the conversion formula for degree to radian conversion as follows:
 From degree to radian = measure of angle in degree \[\times \dfrac{\pi }{180{}^\circ }\] .
Substituting the given measure of angle in degrees, we can find its radian measure.
Measure in radian system = \[-{{105}^{\circ }}\times \dfrac{\pi }{180{}^\circ }\]
Canceling out the common factors from both numerator and denominator, the above expression can be written as,
Measure in radian system = \[-\dfrac{7}{12}\pi \]
We can also convert the above fraction to its decimal form, by dividing the numerator by the denominator as follows.
Measure in radian system \[\approx -0.583\pi \]

Note: The opposite of this conversion, that is from radian to degree measure should also be remembered. The formula for this conversion is:
Measure in degree = measure of angle in radian \[\times \dfrac{180{}^\circ }{\pi }\]. This conversion formula along with the one given above should be remembered.