## anonymous one year ago What is the radian measure of an angle whose degree is 72? Could someone help me please?

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1. mathstudent55

A full circle is an angle of how many degrees?

2. mathstudent55

|dw:1435097177282:dw|

3. mathstudent55

Hint: each quadrant is a right angle, and a right angle is 90 degrees, and there are 4 quadrants.

4. mathstudent55

|dw:1435097281980:dw|

5. anonymous

360?

6. anonymous

(Thank you for helping, by the way)

7. anonymous

But I still do need help

8. LynFran

still need help?

9. LynFran

$72*\frac{ \pi }{ 180 }$ use that and u will get the radian measure

10. anonymous

Thank you!

11. mathstudent55

Yes, a full circle is 360 degrees. Now we need to see how many radians that is. |dw:1435120185238:dw|

12. mathstudent55

Here is a circle with radius 1. The circumference of a circle is $$2 \pi r$$ In this case the circumference of this circle is $$2 \pi$$ The radian measure of an angle is the same as the arc length in a circle of radius 1. That means the circle of radius 1 has an arc length (circumference) and an angkle measure of $$2 \pi$$ radians. Since we know a circle has an angle measure of 360 degrees, that gives us our conversion factor: $$360^o = 2 \pi~radians$$ which can be simplified to $$180^o = \pi~radians$$

13. mathstudent55

Since dividing an number by itself equals 1, and now we know that $$180^o = \pi~rad$$, we can also get: $$\dfrac{180^o}{\pi~rad} = \dfrac{\pi~rad}{180^o} = 1$$ The last two fractions are conversion factors. If you want to convert degrees into radians, multiply by the second fraction, where the degrees cancel out. If you want to convert radians into degrees, multiply by the first fraction in which radians will cancel out.

14. mathstudent55

Examples: 1. Write 90 degrees in radians. Solution: $$90^o \times \dfrac{\pi~rad}{180^o} = \dfrac{\pi}{2} ~rad$$ 2. Write $$\dfrac{3\pi}{2} ~rad$$ in degrees. Solution: $$\dfrac{3\pi}{2} ~rad \times \dfrac{180^o}{\pi~rad} = 270^o$$

15. mathstudent55

Now you can do your problem using 72 deg and the correct conversion factor.