Question

If $x\left(t\right)=3\cos t,y\left(t\right)=2+4\sin t$, what is the approximate value of $x$ when $y=5$?

• A. 1.98
• B. 1.78
• C. 1.58
• D. 1.38
• E. 1.18

Answer 1

The correct option is A 1.98

Given, $x\left(t\right)=3\cos t,y\left(t\right)=2+4\sin t$

When $y=5$, we have $5=2+4\sin t$ $\Rightarrow \sin t=3/4$
Which gives $\cos t=\sqrt{1-{\sin }^{2}t}=\sqrt{1-\frac{9}{16}}=\frac{\sqrt{7}}{4}$
Therefore, $x=3\cos t=\frac{3\sqrt{7}}{4}=1.98$