Question

What is 720° converted to radians? a) 1/4 b) pi/4 c) 4/pi d) 4pi

Answer 1

Answer:

$720^{\circ}=4\pi$

Step-by-step explanation:

Given :$720^{\circ}$

To Find : What is 720° converted to radians?

Solution :

1 degree = $\frac{\pi}{180} radian$

So, $720^{\circ}= \frac{\pi}{180} \times 720$

$720^{\circ}=4\pi$

So, Option D is true

Hence $720^{\circ}=4\pi$

Answer 2

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  

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. What is 270° converted to radians? brainly.com/question/3161884

Keywords: 720° converted to radians, degrees, quadrant, 4π, conversion, multiply by, pi, 180°, revolutions, the formula