Question

Please help me with this calculus problem!



Write the steps to find the equation of the line that is tangent to the graph of y=2sin(x) + sin^2(x) at point (pi/6, 5/4)

i) Is the derivative of the sinusoidal function also periodic?
ii) Does this statement hold true for fifth derivatives?

Answer 1

i) yeah. deriving sine, you get cosine and from that you get -sine and so on.
ii) yes. With Sinusoidal Phenomena, derivatives are only phase shifts as apposed to polynomials.

To Find the tangent at the point you only need to see that the x location: pi/6 at the point of the derivative..
y=2sin(x) + sin^2(x)
=>
y'=2cos(x) + 2sin(x) cos(x)
y'(pi/6)=2cos(pi/6) + 2sin(pi/6) cos(pi/6)
=2(root(3)/2)+2(1/2)*(root(3)/2)
=5/6 * root(3)

Answer 2

THANK YOU SOO MUCH!!