Calculate the area of the shaded region in a unit circle with central angles $ heta $ and $ alpha $

Answer 1

Let’s calculate the area of the shaded region in a unit circle with central angles $ \theta $ and $ \alpha $.

The area of a sector of a circle is given by:

$ A = \frac{1}{2} r^2 \theta $

For a unit circle, $ r = 1 $, so the above formula simplifies to:

$ A = \frac{1}{2} \theta $

The area of the shaded region is then the difference between two sector areas:

$ A_{shaded} = \frac{1}{2} (\theta – \alpha) $

Answer 2

To find the area of the region bounded by two radii in a unit circle with angles $ heta $ and $ alpha $:

The formula for the area of a sector is:

$ A = frac{1}{2} r^2 heta $

For a unit circle, this is:

$ A = frac{1}{2} heta $

The area between the two radii is:

$ A_{region} = frac{1}{2} ( heta – alpha) $

Answer 3

To find the area between two angles $ heta $ and $ alpha $ in a unit circle:

$ A_{area} = frac{1}{2} ( heta – alpha) $

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