Calculus - related rates question
- Thread starter Chewy23
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Hint:
h = 4 * sin(Θ)
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Okay so I have established that I need to find the height of the boom gate with respect to time at theta = pi/3.
I've set out an equation to find the answer which is dh/dt = d(theta)/dt x dh/d(theta). I know that d(theta)/dt = 0.05 from the question, however I don't know how to find d(theta)/dt. I know I need to find an equation and then flip it. But I need help on that bit.
I've set out an equation to find the answer which is dh/dt = d(theta)/dt x dh/d(theta). I know that d(theta)/dt = 0.05 from the question, however I don't know how to find d(theta)/dt. I know I need to find an equation and then flip it. But I need help on that bit.
You have all the ingredients you need to use.
[MATH] \text{ }\\ h=4\sin\theta \text{ (courtesy of Subhotosh Khan)}\\ \therefore \frac{dh}{d\theta}=?? \\ \frac{d\theta}{dt}=0.05 \text{ (courtesy of yourself)}\\ \frac{dh}{dt}=\frac{dh}{d\theta}\frac{d\theta}{dt} \text{ (courtesy of yourself)}\\ \therefore \frac{dh}{dt}=?? \\ \text{and then evaluate the expression for } \frac{dh}{dt} \text{ at }\theta=\tfrac{\pi}{3}[/MATH]
[MATH] \text{ }\\ h=4\sin\theta \text{ (courtesy of Subhotosh Khan)}\\ \therefore \frac{dh}{d\theta}=?? \\ \frac{d\theta}{dt}=0.05 \text{ (courtesy of yourself)}\\ \frac{dh}{dt}=\frac{dh}{d\theta}\frac{d\theta}{dt} \text{ (courtesy of yourself)}\\ \therefore \frac{dh}{dt}=?? \\ \text{and then evaluate the expression for } \frac{dh}{dt} \text{ at }\theta=\tfrac{\pi}{3}[/MATH]