³/₂π or 1.5π radians
Further explanation
We provide an angle of 270° 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 promptly 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 = 270°. Let us convert this degree to radians.
\(\boxed{ \ \alpha = 270^0 \times \frac{\pi }{180^0} \ }\)
270° and 180° crossed out. They can be divided by 90°.
\(\boxed{ \ \alpha = 3 \times \frac{\pi }{2} \ }\)
Hence, \(\boxed{\boxed{ \ 270^0 = \frac{3}{2} \pi \ radians \ }}\)
- - - - - - -
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
- Undefined terms needed to define angles https://brainly.com/question/3717797
Keywords: 270° converted to radians, degrees, quadrant, π, conversion, multiply by, pi, 180°, revolutions, the formula
