Thursday

January 29, 2015

January 29, 2015

Posted by **Penny** on Tuesday, January 24, 2012 at 6:37pm.

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 -
**Steve**, Wednesday, January 25, 2012 at 11:58amWay 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.

**Answer this Question**

**Related Questions**

Trigonometry Help - Simplify: sin(x-y)cosy+cos(x-y)siny = (sinxcosy-cosxsiny)...

Trigonometry - Prove that (cosy/1+siny) + (1+siny/cosy) = 2secy

Trigo help! - Ok, i've tried this question, and it brings me to no answers. ...

calc - what is the derivative of sinx- cosy = 0 in its simplest form? I got to ...

AP Calculus - I previously posted this but had a mistake in it. Determine dy/dx...

trig - Okay, I've been getting some of these, but I can't seem to verify this ...

Calculus - Consider the closed curve in the day plane: 2x^2-2xy+y^3=14 a) show ...

calculus - Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show ...

Calculus - A curve is defined by the parametric equations: x = t2 – t and y = t3...

calculus - Given the curve defined by the equation y=cos^2(x) + sqrt(2)* sin(x) ...