Posted by **holly** on Monday, February 6, 2012 at 11:21pm.

Find the points on the curve below at which the tangent is horizontal. Use n as an arbitrary integer. (Enter your answers as a comma-separated list.)

y = sin x/

2 + cos x

- calculus -
**Reiny**, Monday, February 6, 2012 at 11:39pm
did you mean

y = sinx/(2+cosx) ??

I will assume you did.

dy/dx = ( (2+cosx)(cos) - sinx(-sinx) )/(2+cosx)^2

= (2cosx + cos^2 x + sin^2 x)/(2+cosx)^2

= (1 + 2cosx)/(2+cosx)^2

for a horizontal tangent, dy/dx = 0

or

1 + 2cosx = 0

cosx = -1/2

x = 2π/3 or x = 4π/3 , (120° or 240° )

the period of cosx = 2π

so general solutions:

x = 2π/3 + n(2π) or

x = 4π/3 + n(2π)

## Answer this Question

## Related Questions

- calculus - Find the x-coordinates of all points on the curve f(x) = sin 2x &#...
- calculus - 5) Find the points on the curve below at which the tangent is ...
- Calculus 1 - Find the critical numbers of the function. (Enter your answers as a...
- calculus - For what values of x does the graph of f have a horizontal tangent? (...
- calculus - Solve the given equation. (Enter your answers as a comma-separated ...
- Calculus - Find all values of x in the interval [0, 2π] that satisfy the ...
- calculus - Find the points on the curve y= (cos x)/(2 + sin x) at which the ...
- Calculus - Find all points on the graph of the function f(x) = 2 cos x + cos^2 ...
- Trigonometry - Solve the equation for exact solutions in the interval 0 ≤ ...
- Calculus - We can find some of the solutions of sin x = 0.2 graphically by ...

More Related Questions