Question

An objects motion is described by the equation d= 4sin (pi t) what will the height of the object be at 1.75 seconds?

Answer 1

Answer:

-2√2, or ≈-2.83

Step-by-step explanation:

Well, when t = 1.75, our equation should be $d=4\sin{(\pi \cdot1.75)}$.

Note that $\pi\cdot1.75=\frac{7\pi}{4}$. Using the unit circle (attached), we can find that the value of sine at $\frac{7\pi}{4}$ radians is exactly $-\frac{\sqrt2}{2}$. Plugging that value back into our equation gives us

$d=4\cdot\left(-\frac{\sqrt2}{2} \right)=-\frac{4\sqrt2}{2}=-2\sqrt2$

So our answer is $d=-2\sqrt2$, in whatever units we're using to measure height.