# Calculus

posted by .

Consider the curve defined by y + cosy = x +1 for 0 =< y =< 2pi....

a. Find dy/dx in terms of y. *I got 1/(y-siny) but I feel like that's wrong.

b. Write an equation for each vertical tangent to the curve.

c. find d^2y/dx^2 in terms of y.

d. Sketch a graph of the curve using a table of values for 0 =< y =< 2pi.

Table of values? Vertical tangents? Finding the second derivative? Way out of my league. I'd REALLY appreciate the help!!!

• Calculus -

Way out of your league? Are you taking calculus? These topics should be familiar to you.

a.
y + cosy = x+1
y' - siny y' = 1
y'(1 - siny) = 1
y' = 1/(1 - siny)

b. vertical tangents occur where y' is infinite. That means where the denominator is zero.

1 - siny = 0 where siny = 1, or y = pi/2
when y=pi/2, 5pi/2, ... (4k+1)pi/2
y + cosy = x+1
(4k+1)pi/2 + 0 = x+1
x = (4k+1)pi/2 - 1

so, the vertical tangents are the lines x = (4k+1)pi/2 - 1

c.
y' = 1/(1 - siny)
y'' = 1/(1 - siny)^2 * (-cosy) y'
= -cosy/(1-siny)^2 * 1/(1-siny)
= -cosy/(1-siny)^3

d. go to wolframalpha and type

plot y + cosy = x + 1

and it will show the serpentine curve, making it clear that there are many vertical tangents.

## Similar Questions

1. ### Trigonometry

Prove that (cosy/1+siny) + (1+siny/cosy) = 2secy
2. ### trig

Okay, I've been getting some of these, but I can't seem to verify this identity... any help?
3. ### Trigo help!

Ok, i've tried this question, and it brings me to no answers. Please help! Prove the following: secY(1+tanY)=6cosecY my workings: LeftHandSide: secY + tanY/cosY = 1/cosY + sinY/cos^2Y =(cosY+sinY)/cos^2Y = ?
4. ### Trigonometry Help

Simplify: sin(x-y)cosy+cos(x-y)siny = (sinxcosy-cosxsiny)cosy+(cosxcosy+sinxsiny)siny = ?
5. ### calculus

Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope -1 is tangent to the curve …
6. ### Calculus

Please help this is due tomorrow and I don't know how to Ive missed a lot of school sick Consider the curve given by the equation x^3+3xy^2+y^3=1 a.Find dy/dx b. Write an equation for the tangent line to the curve when x = 0. c. Write …
7. ### calculus

consider g(x)= {a sin x + b, if x ≤ 2pi} {x^2 - pi x + 2, if x > 2pi} A. Find the values of a a b such that g(x) is a differentiable function. B. Write the equation of the tangent line to g(x) at x = 2pi. C. Use the tangent …
8. ### AP AB Calculus

Linear approximation: Consider the curve defined by -8x^2 + 5xy + y^3 = -149 a. find dy/dx b. write an equation for the tangent line to the curve at the point (4,-1) c. There is a number k so that the point (4.2,k) is on the curve. …
9. ### Math

Suppose f(x) = sin(pi*cosx) On any interval where the inverse function y = f –1(x) exists, the derivative of f –1(x) with respect to x is: a)-1/(cos(pi*cosx)), where x and y are related by the equation (satisfy the equation) x=sin(pi*cosy) …
10. ### Calculus AB

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive?

More Similar Questions