Given y = 11 sin (7 pi x - 5 y), verify (4,0) is on line; find tangent, normal at pt

[sumara_feroz]

Given the function y = 11 sin (7 pi x - 5 y) and the point (4,0).

a) Verify that the given point is on curve.
b) Find the equation of the tangent line to the curve at the given point.
c) Find the equation of the normal line to the curve at the given point.

Please guide on how to solve this!

 

[tkhunny]

Have you considered substituting the given values? That would be a good place to start.

 

[sumara_feroz]

Yes, i substituted the values of x and y. But it is not satisfying. I don't understand where I am making mistake.

 

[mmm4444bot]

I don't understand where I am making mistake [for part (a)].

We could probably help you find your mistake, were you to show your work.

y = 11·sin(7·Pi·x - 5·y)

The expression highlighted in red equals zero, when x=4 and y=0. Sine is zero at all integer multiples of Pi. :cool:

 

[stapel]

Given the function y = 11 sin (7 pi x - 5 y) and the point (4,0).

a) Verify that the given point is on curve.
b) Find the equation of the tangent line to the curve at the given point.
c) Find the equation of the normal line to the curve at the given point.

...I substituted the values of x and y. But it is not satisfying. I don't understand where I am making mistake.

Okay; we can't troubleshoot work we can't see. So, rather than making reference to your feelings regarding the end results of your work, please reply showing your work (all of it).

For instance, for part (a), this is just algebra. You plugged the given x-value into the given formula, simplified to find the corresponding value of y, and... then what?

For part (b), you applied the relevant part of differential calculus to the equation, evaluated at the given x-value to find the slope of the curve at the given point, used the slope and the point in the point-slope formula that you'd memorized back in algebra, and... then what?

For part (c), you applied what you learned back in algebra about parallel and perpendicular lines, plugged this into one of the line-equation formulas, and... then what?

Please be complete. Thank you!