Question

Find the slope of the tangent line to the parametric curve.\\ a. $x = 2 \cos(3t) - 4 \sin(3t)$, $y = 3 \tan(6t)$ at $t = \frac{\pi}{2}$\\ b. $x = \frac{t}{2}$, $y = t^2 + 1$ at $t = -1$

          Find the slope of the tangent line to the parametric curve.\\
a. $x = 2 \cos(3t) - 4 \sin(3t)$, $y = 3 \tan(6t)$ at $t = \frac{\pi}{2}$\\
b. $x = \frac{t}{2}$, $y = t^2 + 1$ at $t = -1$

Find the slope of the tangent line to the parametric curve.

a. x = 2 cos(3t) - 4 sin(3t), y = 3 tan(6t) at t = (π)/(2)

b. x = (t)/(2), y = t^2 + 1 at t = -1

Added by Barbara L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Pritesh Ranjan

Step 1

To find the derivative of x with respect to t, we can use the chain rule. The chain rule states that if we have a function of the form f(g(t)), then the derivative of f(g(t)) with respect to t is f'(g(t)) * g'(t). In this case, x = 2cos(3t) - 4sin(3t), so we can Show more…

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