math
posted by deel .
Please help me to find an equation for the tangent to the curve xsin2y=ycos2x at the point (phi/4, phi/2)

math 
Steve
first, it's PI, not PHI
pi(π) = 3.14, the ratio of circumference to diameter
phi(φ) = 1.62 (1+√5)/2, the golden ratio
So, we use implicit differentiation to get
xsin2y = ycos2x
sin2y + 2xcos2y y' = cos2x y'  2ysin2x
y' = (sin2y + 2y sin2x)/(2x cos2y  cos2x)
at (π/4,π/2), that gives a slope of
y' = (0 + π*(1))/(π/2*(1)  0)
= π/(π/2)
= 2
So, bow you want the line with slope=2 through (π/4,π/2):
y  π/2 = 2(x  π/4)
y = 2x 
math 
difference
xsin2y=ycos2x
Respond to this Question
Similar Questions

Precalculs
I have no idea how to do these type of problems. Problem Solve each equation on the interval 0 less than or equal to theta less than 2 pi 42. SQRT(3) sin theta + cos theta = 1  There is an example … 
Physics
The electric flux through each of the six sides of a rectangular box are as follows: phi 1= +150.0 N*m^2/C; phi 2= +250.0 N*m^2/C; phi 3= 350.0 N*m^2/C; phi 4= +175.0 N*m^2/C; phi 5= 100.0 N*m^2/C; phi 6= +450.0 N*m^2/C How much … 
Calculus
Evaluate, in spherical coordinates, the triple integral of f(rho,theta,phi)=cos (phi) , over the region 3<rho<7, 0<theta<2pi, 0<phi<pi/3. I used the equation cos (phi)*sin(phi)*rho d(rho)d(phi)d(theta) with the given … 
Algebra
Let \phi(n) be the Euler Phi Function. If 1 \leq n \leq 1000, what is the smallest integer value of n that minimizes \frac{\phi(n)}{n}? 
precalculus PLEASE HELP!!
Rewrite 4 sin(x) 1 cos(x) as A sin(x + phi) A= phi= pi less than phi less than pi 
Trigonometry  Slopes stuff
Point A is the terminal point of angle phi and point B is the terminal point of angle theta. Point A is in the first quadrant and point B is in the second quadrant, while tan phi = 1 and tan theta = 7. Find the slope of AB. Ok so … 
maths
If sin(theta)=3/5 , tan(phi)= 1/2 and 90¡ã< theta <180¡ã<phi< 270¡ã, find tha value of 8tan(theta)  5^1/2 sec(phi) 
math (integration)
I'm being asked to find a value at one specific point, pi, what would be my limits? 
physics simple harmonic motion
A particle moving in simple harmonic motion passes through the equilibrium point (x=0) 8 times per second. At t=0 its velocity at x=0.015m is negative. It travels 0.6m in a complete cycle. The particle's position as a function of time … 
Calculus AB
Could someone please help me with these tangent line problems?