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单位圆
角的弧度度量是什么？
1. Introduction
Introduction
2. Radians and degrees
Radians and degrees
3. Special points on the unit circle
Special points on the unit circle
4. Special points and arc length in non-unit circles
Special points and arc length in non-unit circles
5. Radian spacing on the unit circle
Twenty-four equally spaced points divide the unit circle. What central distance separates consecutive points?
6. Converting thirty degrees
How many degrees is the angle pi/6 radians? Give the exact integer.
7. Converting two pi over three
How many degrees is the angle 2pi/3 radians? Give the exact integer.
8. Converting 240 degrees
How many radians is 240 degrees? Give the exact value as a multiple of pi, written as a fraction: enter the numerator over the denominator.
9. Sides of the isosceles right triangle
A 45-45-90 triangle has hypotenuse 1. What are its equal legs?
10. Sides of the 30-60-90 triangle
A 30-60-90 triangle has hypotenuse 1 with the longer leg along the x-axis. What are the two legs, and what are the unit-circle coordinates at pi/3?
11. Arc length on a radius-eleven circle
On a circle of radius 11, what is the arc length intercepted by a central angle of 5pi/3? Give the exact value as a multiple of pi, numerator over denominator.
12. Radius from arc length and angle
An angle of 7pi/6 intercepts an arc of length pi/2. What is the radius? Give the exact fraction.
13. Lengths scale by the radius
An arc intercepted by a central angle of pi/3 on a circle of radius 6 has length 2pi.