Question

suppose an arc of length s lies on the unit circle x² + y² = 1, starting at the point (1,0) and terminating at the point (x,y). use a calculator to find the approximate coordinates for (x,y)
s = - 2.1

Explanation:

Step1: Recall unit - circle formulas

For a unit circle \(x^{2}+y^{2}=1\), if an arc of length \(s\) starts at \((1,0)\) and terminates at \((x,y)\), then \(x = \cos s\) and \(y=\sin s\).

Step2: Substitute \(s=- 21\) into the formulas

We know \(x=\cos(-21)\) and \(y = \sin(-21)\). Using a calculator in radian mode:
\(x=\cos(-21)\approx - 0.5048\)
\(y=\sin(-21)\approx - 0.8632\)

Answer:

\((-0.5048,-0.8632)\)