Tuesday

January 27, 2015

January 27, 2015

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

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 6:44pmusing 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 - Given the curve defined by the equation y=cos^2(x) + sqrt(2)* sin(x) ...

calculus - 5) Find the points on the curve below at which the tangent is ...

Calculus 12th grade (double check my work please) - 1.)Find dy/dx when y= Ln (...

calculus - Find the points on the curve below at which the tangent is horizontal...

Calculus - Consider the curve y^2+xy+x^2=15. What is dy/dx? Find the two points ...

calculus help - Find the points where the tangent line is horizontal or vertical...

calculus help please - Find the points where the tangent line is horizontal or ...

calculus - Find the x-coordinates of all points on the curve f(x) = sin 2x &#...

maths - Find the x-coordinates of all points on the curve y=2sin-sin^2x at ...