Question

Find all values of $t$ in $(-\pi, \pi)$ for which the tangent line to the graph of $x(t) = t - 2\cos t$, $y(t) = t + 2\cos t$, is vertical. 1. $t = -\frac{\pi}{3}, \frac{\pi}{3}$ 2. $t = -\frac{\pi}{6}, \frac{5\pi}{6}$ 3. $t = -\frac{5\pi}{6}, \frac{\pi}{6}$ 4. $t = -\frac{\pi}{6}, \frac{\pi}{6}$ 5. $t = -\frac{2\pi}{3}, \frac{\pi}{3}$ 6. $t = \frac{\pi}{3}, \frac{2\pi}{3}$

          Find all values of $t$ in $(-\pi, \pi)$ for which the tangent line to the graph of
$x(t) = t - 2\cos t$,
$y(t) = t + 2\cos t$,
is vertical.
1. $t = -\frac{\pi}{3}, \frac{\pi}{3}$
2. $t = -\frac{\pi}{6}, \frac{5\pi}{6}$
3. $t = -\frac{5\pi}{6}, \frac{\pi}{6}$
4. $t = -\frac{\pi}{6}, \frac{\pi}{6}$
5. $t = -\frac{2\pi}{3}, \frac{\pi}{3}$
6. $t = \frac{\pi}{3}, \frac{2\pi}{3}$

Find all values of t in (-π, π) for which the tangent line to the graph of
x(t) = t - 2cos t,
y(t) = t + 2cos t,
is vertical.
1. t = -(π)/(3), (π)/(3)
2. t = -(π)/(6), (5π)/(6)
3. t = -(5π)/(6), (π)/(6)
4. t = -(π)/(6), (π)/(6)
5. t = -(2π)/(3), (π)/(3)
6. t = (π)/(3), (2π)/(3)

Added by William J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Linh Vu

08/20/2020

Step 1

This is because a vertical tangent line corresponds to a slope that is undefined. Show more…

Show all steps

Thanks for your feedback!

Find all values of t in (-π, π) for which the tangent line to the graph of x(t) = t - 2cos(t), y(t) = t + 2cos(t), is vertical. t = -(π)/3, (π)/3 t = (π)/6, (5π)/6 t = -(5π)/6, -(π)/6 t = -(π)/6, (π)/6 t = -(2π)/3, (π)/3 t = (π)/3, (2π)/3 Find all values of t in (-T,) for which the tangent line to the graph of t = t - 2cos(t) u = t + 2cos(t) is vertical. 1. t TT TT 3 3 TT 5TT 2. t 9 6 5TT TT 3. t 6 TT TT 4. t = 6 6 2TT T 5. t 3 3 TT 2TT 6. t = 3 3