find the x coordinates of all the points on the curve y=tanx, x€ (0,pi), where the tangent line is parallel to the line y= (4(x+pi)) / 3.

Question

I have a calculus test tomorrow please help!!

Thank you

Answer 1

Parallel lines have the same slope.

slope of y = (4/3)(x + π) is 4/3.

Slope of tangent line to the curve y = tanx at (x, tanx) is y'.

y' = sec²x

So, sec²x = 4/3.

Therefore, cos²x = 3/4

So, cosx = ±√3/2

Solutions in the interval (0, π): x = π/6, 5π/6