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An object is released from the spaceship at x= pi/3 and travels along a line tangent to the graph of y=3cosx towards the x-axis.

a) At what point x will the object strike the x axis?

b) At what angle theta will the object strike the x axis?

I don't even know how to start on this one!

Elsa
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Differentiating $3\cos(x)$ and substituting $\frac{\pi}{3}$ will give you the slope of the tangent line at this point. Can you take it from there?

  • I understand that, but why do I need the slope of the tangent line? – Elsa Nov 17 '14 at 09:06
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    Using the slope, you can immediately obtain the angle $\theta$ (just plug it into the arctangent function), solving b), and also set up a linear equation which will give you the answer to a). –  Nov 17 '14 at 09:08
  • okay so i got the slope to be (-3(3)^1/2)/(2) and why do I plug it to arctangent? is it because it's a tangent line slope? – Elsa Nov 17 '14 at 09:11
  • @Kaaagome: The arctangent function is the inverse of the tangent function. The tangent function of an angle gives the slope, so the arctangent function of a slope gives the angle. –  Nov 17 '14 at 09:12
  • oh! i didn't realize that! thank you! the linear equation is just the slope, the x, and the y, right? thank you so much again! – Elsa Nov 17 '14 at 09:15
  • @Kaaagome: That's right, $ax+y$, where $a$ is the slope. –  Nov 17 '14 at 09:17