4π radians
We provide an angle of 720° that will be instantly converted to radians.
Recognize these:
From the conversion previous we can produce the formula as follows:
We can state the following:
Given α = 720°. Let us convert this degree to radians.
[tex]\boxed{ \ \alpha = 720^0 \times \frac{\pi }{180^0} \ }[/tex]
720° and 180° crossed out. They can be divided by 180°.
[tex]\boxed{ \ \alpha = 4 \times \pi \ }[/tex]
Hence, [tex]\boxed{\boxed{ \ 720^0 = 4 \pi \ radians \ }}[/tex]
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Another example:
Convert [tex]\boxed{ \ \frac{4}{3} \pi \ radians \ }[/tex] to degrees.
[tex]\alpha = \frac{4}{3} \pi \ radians \rightarrow \alpha = \frac{4}{3} \pi \times \frac{180^0}{\pi }[/tex]
180° and 3 crossed out. Likewise with π.
Thus, [tex]\boxed{\boxed{ \ \frac{4}{3} \pi \ radians = 240^0 \ }}[/tex]
Keywords: 720° converted to radians, degrees, quadrant, 4π, conversion, multiply by, pi, 180°, revolutions, the formula
Answer:
[tex]720^{\circ}=4\pi[/tex]
Step-by-step explanation:
Given :[tex]720^{\circ}[/tex]
To Find : What is 720° converted to radians?
Solution :
1 degree = [tex]\frac{\pi}{180} radian[/tex]
So, [tex]720^{\circ}= \frac{\pi}{180} \times 720[/tex]
[tex]720^{\circ}=4\pi[/tex]
So, Option D is true
Hence [tex]720^{\circ}=4\pi[/tex]
