4π radians
Further explanation
We provide an angle of 720° that will be instantly converted to radians.
Recognize these:
- \(\boxed{ \ 1 \ revolution = 360 \ degrees = 2 \pi \ radians \ }\)
- \(\boxed{ \ 0.5 \ revolutions = 180 \ degrees = \pi \ radians \ }\)
From the conversion previous we can produce the formula as follows:
- \(\boxed{\boxed{ \ Radians = degrees \times \bigg( \frac{\pi }{180^0} \bigg) \ }}\)
- \(\boxed{\boxed{ \ Degrees = radians \times \bigg( \frac{180^0}{\pi } \bigg) \ }}\)
We can state the following:
- Degrees to radians, multiply by \(\frac{\pi }{180^0}\)
- Radians to degrees, multiply by \(\frac{180^0}{\pi }\)
Given α = 720°. Let us convert this degree to radians.
\(\boxed{ \ \alpha = 720^0 \times \frac{\pi }{180^0} \ }\)
720° and 180° crossed out. They can be divided by 180°.
\(\boxed{ \ \alpha = 4 \times \pi \ }\)
Hence, \(\boxed{\boxed{ \ 720^0 = 4 \pi \ radians \ }}\)
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Another example:
Convert \(\boxed{ \ \frac{4}{3} \pi \ radians \ }\) to degrees.
\(\alpha = \frac{4}{3} \pi \ radians \rightarrow \alpha = \frac{4}{3} \pi \times \frac{180^0}{\pi }\)
180° and 3 crossed out. Likewise with π.
Thus, \(\boxed{\boxed{ \ \frac{4}{3} \pi \ radians = 240^0 \ }}\)
Learn more
- A triangle is rotated 90° about the origin https://brainly.com/question/2992432
- The coordinates of the image of the point B after the triangle ABC is rotated 270° about the origin https://brainly.com/question/7437053
- What is 270° converted to radians? https://brainly.com/question/3161884
Keywords: 720° converted to radians, degrees, quadrant, 4π, conversion, multiply by, pi, 180°, revolutions, the formula
