SOLUTION: Hi Can somebody please help with this If x = a cos^3 theta and y = b sin^3 theta, a and b constants, show that when theta = pi/4, dy/dx = -b/a. Thanks in advance

Algebra ->  Length-and-distance -> SOLUTION: Hi Can somebody please help with this If x = a cos^3 theta and y = b sin^3 theta, a and b constants, show that when theta = pi/4, dy/dx = -b/a. Thanks in advance      Log On


   

Question 377575: Hi Can somebody please help with this
If x = a cos^3 theta and y = b sin^3 theta, a and b constants, show that when theta = pi/4, dy/dx = -b/a.
Thanks in advance
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x=a%28cos%28theta%29%29%5E3
dx%2Fd%28theta%29=3a%28cos%28theta%29%29%5E2%2A%28-sin%28theta%29%29
dx%2Fd%28theta%29=-3a%28cos%28theta%29%29%5E2%2Asin%28theta%29
.
.
.
y=b%28sin%28theta%29%29%5E3
dy%2Fd%28theta%29=3b%28sin%28theta%29%29%5E2%2Acos%28theta%29
.
.
dy%2Fdx=%28dy%2Fd%28theta%29%29%2F%28dx%2Fd%28theta%29%29
dy%2Fdx=-%28%283b%29%2F%283a%29%29%28tan%28theta%29%29%5E2%2A%281%2Ftan%28theta%29%29
dy%2Fdx=-%28b%2Fa%29tan%28theta%29
When theta=pi%2F4, tan%28pi%2F4%29=1
highlight%28dy%2Fdx=-%28b%2Fa%29%29