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Trig Identity (4) - Geometric Investigation

Drag the point on the semicircle anywhere you can. Then slide the slider slowly.

What is the area of the square in the upper left corner?

What is the area of the shaded rectangle on the bottom right (in terms of θ)?

What is the area of the unshaded rectangle on the bottom left (in terms of θ)?

Write an equation that describes the relationship among these 3 areas from the animation you saw above.

Quick silent demo