Problem 1106

Convert the angle in radians to degrees. Express your answer in decimal form.

5.63

 

Solution:-

 

Consider a circle of radius r. A central angle of a revolution (360°) will subtend an arc equal to the circumference of the circle. Because the circumference of the circle equal 2πr, we see that 360° = 2π radians, or 180° = π radians. Dividing both sides by π, we have the following conversion formula.

Converting form radians to degrees can be summarized as follows.

1 radian = \frac{180}{\pi} degrees

Therefore, the following is true.

5.63 radians = 5.63 * 1 radian

= 5.63 *\frac{180}{\pi} degrees

\approx 322.58°

 

 

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