Question

What is 270° converted to radians?

Answer 1

Answer:

$\frac{3\pi}{2}$

Step-by-step explanation:

The radian is a unit of angle in the plane in the IUS (international system of units)

Where the number pi equals 180 degrees

To calculate how many radians 270 degrees equal we apply a simple rule of three

$180\º \longrightarrow \pi \\270\º \longrightarrow x\\x=\frac{270.\pi}{180} =\frac{3\pi}{2}$

Answer 2

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, $\boxed{\boxed{ \ 270^0 = \frac{3}{2} \pi \ radians \ }}$

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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

1. A triangle is rotated 90° about the origin brainly.com/question/2992432
2. The coordinates of the image of the point B after the triangle ABC is rotated 270° about the origin brainly.com/question/7437053  
3. Undefined terms needed to define angles brainly.com/question/3717797

Keywords: 270° converted to radians, degrees, quadrant, π, conversion, multiply by, pi, 180°, revolutions, the formula