# re: Differential Calculus

Write the equation of lines tangent and normal to the following function at (0, π). To find derivative, use implicit differentiation.

x^2cos^2y - siny = 0

Note: I forgot the ^2 for cos on the previous question. Sorry.

1. 👍
2. 👎
3. 👁
1. x = 0, y = pi

-x^2 2 cos y sin y dy +cos^2y 2 x dx - cos y dy = 0

2 cos^2 y x dx=cosy (2x^2siny+1)dy

dy/dx = slope m

m = 2 x cos y/(2x^2siny+1)
at (0,pi)
m = 2 * 0 = 0 Oh my :) horizontal there
so what is y at x = 0 and y = pi
LOL, zero
so along the x axis

1. 👍
2. 👎
2. I mean parallel to x axis and y = pi
for part 2, normal is up the y axis
see
http://www.wolframalpha.com/widgets/view.jsp?id=91851988c40ebbe236f5561e167c9ab8

1. 👍
2. 👎
3. Just copy your function into there:
x^2cos^2y - siny = 0

look at the solution close to (0,0)

1. 👍
2. 👎

## Similar Questions

1. ### math

Draw a diagram to show that there are two tangent lines to the parabola y = x2 that pass through the point (0, −25). Find the coordinates of the points where these tangent lines intersect the parabola.

2. ### Calculus

The line that is normal to the curve x^2=2xy-3y^2=0 at(1,1) intersects the curve at what other point? Please help. Thanks in advance. We have x2=2xy - 3y2 = 0 Are there supposed to be 2 equal signs in this expression or is it x2 +

3. ### calculus

Find equations for the lines that are tangent and normal to the graph of y = sinx + 3 at x = pi

4. ### Calculus - Functions?

#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2 a.) Find the values of

1. ### Calculus

Draw a diagram to show that there are two tangent lines to the parabola y=x^2 that pass through the point (0,-4). Find the coordinates of the points where these tangent lines intersect the parabola. So far I have taken the

2. ### Calc

Let f be the function given by f(x) = tan x and let g be the function given by g(x) = x^2. At what value of x in the interval 0≤x≤π do the graphs of f and g have parallel tangent lines?

3. ### Calculus

a)The curve with equation: 2y^3 + y^2 - y^5 = x^4 - 2x^3 + x^2 has been linked to a bouncing wagon. Use a computer algebra system to graph this curve and discover why. b)At how many points does this curve have horizontal tangent

4. ### calculus

5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. Find the x coordinate of the point where the tangent line is parallel to the

1. ### Calculus (Urgent Help)

The graph of y=cos x * ln cos^2x has seven horizontal tangent lines on the interval [0,2pi]. Find the x-coordinate of all points at which these tangent lines occur.

2. ### Mathematics

Use implicit differentiation to find the points where the parabola defined by x2−2xy+y2−4y+4=0 has horizontal and vertical tangent lines. The parabola has horizontal tangent lines at the point(s) (x-y)/x-y+2 . The parabola has

3. ### CALCULUS HELP

Write the equation of the tangent line to the graph of the function at the indicated point. Check the reasonableness of your answer by graphing both the function and the tangent line. Y=(x-2)/(15-x^2) x=-4 HOW DO WE DO THIS

4. ### Calculus

Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis