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Question

donnie1999 · Answer

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mathstudent55 · Answer

Take each radian measurement and convert to degrees.

mathstudent55 · Answer

This is how you find the conversion factors:

$2 \pi ~radians = 360^\circ$

Divide both sides by $2 \pi ~radians$

$\dfrac{2 \pi ~radians}{2 \pi~radians} = \dfrac{360^\circ}{2 \pi~radians}$

On the left side, 2 pi rad divided by itself is 1.

$1 = \dfrac{360^\circ}{2 \pi~radians}$

We can reduce the fraction on the right side:

$1 = \dfrac{180^\circ}{\pi~radians}$

If we take the reciprocals of both sides we have:

$1 = \dfrac{\pi~radians}{180^\circ}$

Notice that the last two equations have 1 on the left side, so we can write:

$\dfrac{\pi~radians}{180^\circ} =\dfrac{180^\circ}{\pi~radians} = 1 $

donnie1999 · Answer

ohh ok can you use 23pi/4 as an example

mathstudent55 · Answer

The last line above is what you need.
You have two fractions that equal 1.
You know that multiplying a number by 1 does not change the number.

If you multiply a radian measure by the fraction with degrees in the numerator and radians in the denominator, you end up with degrees.

If you multiply a degree measure by the fraction with radians in the numerator and degrees in the denominator, you end up with radians.

mathstudent55 · Answer

Here are the conversion factors:

To convert radians to degrees, multiply a radian measure by $\dfrac{180^\circ}{\pi~radians} $

To convert degrees to radians, multiply a degree measure by $\dfrac{\pi ~radians}{180^\circ}$

mathstudent55 · Answer

Ok, now let's do the first one as an example.

You have radians, and you want degrees.
You need to cancel radians and end up with degrees.
That means you must multiply by the conversion fraction with degrees in the numerator and radians in the denominator so the radians will cancel out, and you will end up with degrees.

Start here:

$\dfrac{23 \pi}{4} $

mathstudent55 · Answer

Now we pick the correct conversion fraction:

$\dfrac{23 \pi ~\cancel{radians}}{4} \times \dfrac{180^\circ}{\pi~\cancel{radians}} =$

$=\dfrac{23 \cancel{\pi} \times 180^\circ}{4} =\dfrac{23 \cancel{\pi} \times \cancel{180}^\circ~45}{\cancel{4}~~1}  = 1035^\circ$

donnie1999 · Answer

I got that same answer but that not a choice, what do i do ?

mathstudent55 · Answer

We get 1035 degrees.
They want all degree measures to be less than or equal to 360, so we subtract 360 degrees from 1035 degrees as many time3s as needed until the measure is less than 360 deg.

1035 - 360 = 675 (still greater than 360)
675 - 360 = 315 (less than 360; this is the answer)

$\dfrac{23 \pi}{4} ~rad = 315^\circ$

donnie1999 · Answer

ohh ok let me try one my self.

mathstudent55 · Answer

Remember that any angle you have in standard position, when you add or subtract a multiple of 360 degrees, will give you a coterminal angle since 360 degrees is a full circle.

mathstudent55 · Answer

Did you try the second one?

donnie1999 · Answer

so 18pi/5 =288?

mathstudent55 · Answer

Correct.

donnie1999 · Answer

thanks:D

mathstudent55 · Answer

You're welcome.