vrotterigzl

2022-06-24

Point C moves along the top arc of a circle of radius 1 centered at the origin O(0, 0) from point A(-1, 0) to point B(1, 0) such that the angle BOC decreases at a constant rate 1 radian per minute. How does the area of the triangle ABC change at the moment when |AC|=1? Answer: it increases at 1/2 square units per minute. Could you give me a hint how to solve this task? I don't even know what to begin with.

stigliy0

Beginner2022-06-25Added 21 answers

Say angle $BOC$ is $\theta $. Express the area of triangle $ABC$ in terms of $\theta $ (use sin). This is an area $A$ in terms of $\theta $. Find $\frac{dA}{d\theta}$.Then find the point where $CA=1$ and determine $\theta $ at that point. Evaluate $\frac{dA}{d\theta}$ for that value of $\theta $.

polivijuye

Beginner2022-06-26Added 16 answers

and then use the chain rule to obtain $\frac{dA}{dt}=\frac{dA}{d\theta}\ast \frac{d\theta}{dt}$

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