Radian Measure - Investigation
Question 1
Rearrange the arc length formula to find an equation for s/r. This is the radian measure, defined as the ratio of the arc length to the radius.
Adjust the angle slider to change the angle measure. What do you notice about the radian measure for each angle?
Question 2
Adjust the angle measure. What is true about the value of the arc length (s) divided by the radius (r)?
Question 2
How does this relate to circle similarity?
Question 3
Explain how you can find an arc length of a circle given radians extended by the arc and the radius of a circle.
Question 4
a) Estimate the number radians in a semi-circle b) Estimate the number of radians in a full circle
Task 3: Watch the video below to answer questions that follows.
Question 5
If is the angle in radian, what will be the general formula for calculating arc length in terms of radians and radius of the circle.
Question 6: AREA OF SECTOR OF A CIRCLE
Using the video and and the image above, and considering that the area of a sector is given by . If is the angle in radian, what will be the general formula for calculating area of a sector of a circle in terms of radians and radius of the circle.
Question 7: Using your derived formulas, answer the following question. You can check your answers using the established formulas.
Consider a circle with a radius of 4 cm. Calculate the length of the arc and the area of the sector formed by a central angle of 1.5 radians.