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3 years ago

Please help with this simple trig problem- angle of two sectors of a circle

Mathematics

1 answer:

igomit [66]3 years ago

4 0

Answer:

K = (1/2)r^2(sin(θ) +θ)

Step-by-step explanation:

The area of the triangle to the left is ...

A1 = (1/2)r^2·sin(180°-θ) = (1/2)r^2·sin(θ)

The area of the sector to the right is ...

A2 = (1/2)r^2θ

so the total area of the blue shaded region is ...

K = A1 + A2 = (1/2)r^2·sin(θ) + (1/2)r^2·θ

K = (1/2)r^2(sin(θ) +θ)

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