AP Precalculus Quiz
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TRIGONOMETRIC AND POLAR FUNCTIONS
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An Earth-observing satellite's distance from a tracking station is approximated in polar coordinates by r(θ)=20+5sin⁡(2θ)r(\theta)=20+5\sin(2\theta), where rr (thousands of km) is distance from the station and θ\theta (radians) is the satellite's angular position. The derivative drdθ\dfrac{dr}{d\theta} measures how the satellite's distance changes per radian of orbital angle. Because the sine input is 2θ2\theta, the chain rule is required: ddθ[sin⁡(2θ)]=2cos⁡(2θ)\dfrac{d}{d\theta}[\sin(2\theta)]=2\cos(2\theta). Interpret the meaning of the rate of change of r(θ)=20+5sin⁡(2θ)r(\theta)=20+5\sin(2\theta) at θ=0\theta=0 in this satellite-tracking context.​
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