Trig ID (2) - Geometric Investigation

Author:
Tim Brzezinski
Topic:
Cosine, Geometry, Sine, Trigonometric Functions, Trigonometry
Drag the slider up slowly. As you do, pay attention to the phenomena occurring here. After resetting the slider, be sure to change the location of the LARGE POINT (on the semicircle) before re-sliding it again. Note: In this animation, lines that appear to be parallel ARE parallel.

What is the relationship among the areas of the two squares and rectangle shown? Describe.

What is the area of the square on the left in terms of θ?

What is the area of the empty square (bottom left) in terms of θ?

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

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

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