Tuesday

September 30, 2014

September 30, 2014

Posted by **Laura** on Tuesday, April 16, 2013 at 10:42pm.

x=sin(t); y=(cos(t))^2; t=(pi/3)

- Calculus -
**Reiny**, Tuesday, April 16, 2013 at 11:12pmx = sin t

dx/dt = cost

y = cos^2 t

dy/dt = 2cost(-sint) = -2sint cost

slope = dy/dx = (dy/dt) / (dx/dt

= cost/(-2sintcost) = -1/(2sint)

when t = π/3

dy/dt = -1/2sin(π/3) = -1/(2√3/2) = -1/√3

when t = π/3 , x = sin π/3 = √3/2

and y = cos^2 (π/3) = 1/4

so we have a point (√3/2 , 1/4) with slope √3/2

y - 1/4 = (√3/2)(x-√3/2)

2y - 1/2 = √3x - 3/4

√3x - 2y = 1/4

**Answer this Question**

**Related Questions**

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

Calculus AB - Find the equation of the line tangent to the curve at t=pi/3: a) x...

calculus - y sin 12x = x cos 2y, (pi/2, pi/4) Find the tangent line to the curve...

Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...

Calculus - Find an equation of the tangent line to the curve at the given point...

calculus - Find the points on the curve y= (cos x)/(2 + sin x) at which the ...

Calculus - Find an equation of the tangent line to the curve at the given point...

calculus - find tangent line equation to the curve at the given point: y= 7e^x ...

Calculus - Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2y-x...

Calculus - Find an equation of the tangent line to the curve for the given value...