Question

Find an equation of the tangent to the curve at the given pointx=cos(t)+cos(2t)y=sin(t)+sin(2t)(-1,1)y=?

Answer 1

y = -0.11x + 0.89

Explanation:

First find the slope of the tangent line, which is equal to dy/dx

Find the derivative of y at 1:

dy = cos(t) + 2cos(2t)

dy = cos(1) + 2cos(2)

dy = -0.292

Then the derivative of x at -1:

dx = -sin(t) - 2sin(2t)

dx = -sin(-1) - 2sin(-2)

dx = 2.66

So now calculate dy/dx:

dy/dx = -0.11

Now use point slope form to find the equation of the tangent line:

y - 1 = -0.11(x + 1)

y - 1 = -0.11x - 0.11

y = -0.11x + 0.89