How do you find the radian measure formula for angle θ
The radian measure of an angle θ is defined as the ratio of the length of the arc s subtended by θ on a unit circle to the radius r of the circle
The radian measure of an angle θ is defined as the ratio of the length of the arc s subtended by θ on a unit circle to the radius r of the circle.
To find the radian measure formula for angle θ, we can use the definition of radian measure and the formula for the circumference of a circle.
The circumference of a circle can be calculated using the formula:
C = 2πr
where C represents the circumference and r is the radius of the circle.
Now, let’s consider an angle θ that subtends an arc s on a unit circle.
Since the radius of a unit circle is 1, we can substitute r = 1 into the formula for the circumference:
C = 2π(1)
C = 2π
Since the circumference of a unit circle is equal to 2π, we can equate it to the length of the arc s:
2π = s
Now, we can substitute the value of s into the definition of radian measure:
θ = s/r
θ = 2π/1
θ = 2π
Therefore, the radian measure formula for angle θ is θ = 2π.
In summary, the radian measure of an angle θ is equal to 2π, where θ is the central angle subtended by an arc of length equal to the circumference of a unit circle.
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