Posted by **khela** on Thursday, October 28, 2010 at 6:12pm.

find the points to the curve

y=(cos x)/ (2 + sin x)

at which the tangent is horizontal...

can you explain how get the answer thoroughly and step by step...

- math -
**Reiny**, Thursday, October 28, 2010 at 6:44pm
using the quotient rule,

dydx = [(2+sinx)(-sinx) - cosx(cosx)]/(2+sinx)^2

a horizontal tangent implies the slope is zero, that is, the derivative is zero.

(2+sinx)(-sinx) - cosx(cosx) = 0

-2sinx - sin^2x - cos^2x = 0

-2sinx - (sin^2x + cos^2x) = 0

-2sinx - 1 = 0

sinx = -1/2

x = 7π/6 or x = 11π/6 ..... (210° or 330°)

sub 7π/6 and 11π/6 into the original equation to find the corresponding y values.

Those will give you the points in the domain 0 ≤ x ≤ 2π

## Answer This Question

## Related Questions

- calculus - Find the points on the curve y= (cos x)/(2 + sin x) at which the ...
- Calculus - The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), ...
- calculus - Given the curve defined by the equation y=cos^2(x) + sqrt(2)* sin(x) ...
- Calculus 12th grade (double check my work please) - 1.)Find dy/dx when y= Ln (...
- Calculus - Find the equation of the tangent to the curve y=2-e^-x at the point ...
- Trig - sum and difference formulas - Write the expression as a single ...
- Math- Calc 1 - 1. At what point does the normal line to the curve x^2 - XY + Y^2...
- calculus - 5) Find the points on the curve below at which the tangent is ...
- Math - y=arccos(sin(x)), find dy/dx and sketch it's graph(I guess I can do this ...
- calculus - Find the points on the curve below at which the tangent is horizontal...

More Related Questions