In Exercises 29–34, convert each angle in degrees to radians. ...

Question

In Exercises 29–34, convert each angle in degrees to radians. Round to two decimal places. 18°

Accepted Answer

Hey, everyone in this problem, we're asked to write the angle given below in radiance and to round the answer to two decimal places, the angle we're given is 24 degrees. And we have four answer choices all in radiance. Option A 0.41, option B 0.32, option C 0.43 and option D 0.42. Now, what we have here is 24 degrees. OK? And we wanna know what that is equal to in radiance and we're gonna call that value X. So we have X is equal to 24 degrees. OK? These two have to be equivalent. What this really is is just a unit converted, we're converting from degrees into radiant just like we would with any other units. OK? So we're not gonna treat this any differently, but we have to remember the relationship between degrees and radiance. OK? So recall that 180 degrees is equivalent to pi radiance. OK? So when we want to convert our degrees, we have degrees in the numerator, but we want to eliminate that degrees. So we need to do is multiply by something where we have degrees in the denominator. So we're gonna multiply by 180 degrees. Sorry, we're gonna multiply by something with 180 degrees in the denominator and in the numerator, we're gonna have pi radiance, ok? So we have 24 degrees multiplied by pi radiance divided by 180 degrees. Now, we've just stated that pi radiant and 180 degrees are equivalent, they are equal. So this is like multiplying by one which does not change the value of our original angle, which is why we can go ahead and do this. OK? Now that unit of degrees is gonna cancel up or divide out. We're left with X is equal to 24 divided by 180 multiplied by pi radiance. And we can simplify this and write it a 0.41 89 radiant. OK? Now the answer choices want us to round to two decimal places. So if we round this to two decimal places, this is gonna be equal to 0.42 radiant which corresponds with answer choice D. That's it for this one. Thanks everyone for watching. I hope this video helped.

In Exercises 29–34, convert each angle in degrees to radians. Round to two decimal places. 18°

Key Concepts

Degree to Radian Conversion

Understanding Radians

Rounding and Approximation

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