Question

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

Answer 1

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)