Question

Find an equation of the tangent line at the point specified. y = sin t 5 + 5 cos t , t = π 3

Answer 1

\[\frac{ d }{ dt }[\sin(t/5) + 5\cos(t)]\] \[=(1/5)\cos(t/5) - 5\sin(t)\]Now substitute t=pi/3 to get (1/5)(1/2) - √3/2 = 1/10 - √3/2.
This is the slope of the tangent line. Substitute t=pi/3 in the original equation to find the value of y at t=pi/3. Then form the point-slope equation.

Answer 2

Oops. Sorry. Substituting pi/3 in the derivative will give (1/5)cos(pi/18) - 5sin(pi/3). Dunno what cos(pi/18) is. Use a calculator