Question

Find the slope of the graph of the function at the given point.
Function: g(t)=2+3 cos t
Point: (pi, -1)

Answer 1

@DDCamp

Answer 2

First step is to find the derivative at t = pi.
What's the derivative of 2+3cos(t)?

Answer 3

its -3sin(t)

Answer 4

OK.
The tangent line is the line that passes through a graph, but has the same slope of the graph at that point.
What would the slope of g(x) be at t=pi?

Answer 5

Hmmm...I have no idea

Answer 6

-3sin/pi?

Answer 7

@DDCamp

Answer 8

Yes, -3sin(pi)
sin(pi) = 0, so the slope of the tangent line is 0 at (pi, -1)

Answer 9

Now that you know the slope, and you have a point, you can plug this into point-slope form:
y-y₁ = m(x-x₁)
y-(-1) = 0(x-pi)
y+1 = 0
y = -1

Answer 10

Sorry, I have to go now. Good luck with the rest of your work.

Answer 11

Wow thank you! So my answer would be y=-1?

Answer 12

Or is that just the check?