Question

Parametric Differentiation

x= cos^3 theta, y = sin^3 theta
theta = pi/4 (45 degrees)

Find dy/dx and evaluate the specified value of the parameter

Answer 1

ok i just want to check my answer i got \[\sqrt{3}/12\]

Answer 2

Let me get a piece of paper, 2 seconds

Answer 3

\[dy/dx = 3\cos \theta (\sin \theta)^{2}/-3\sin (\cos \theta )^{2}\]

Answer 4

ok

Answer 5

\[\sqrt{3}/-6\]

Answer 6

\[dy/dx=(3\sin^2(\theta)\cos(\theta))/(-3(\cos^2(\theta)\sin(\theta))\]

Answer 7

evaluating I get -1

Answer 8

u have your derivatives mixed the cos is squared in the numerator

Answer 9

or do it? 1 sec

Answer 10

\[dy/dx=-\sin(\theta)/\cos(\theta)=-\tan(\theta)\rightarrow-\tan(\pi/4)=-1\]

Answer 11

hmm

Answer 12

i see what i did wrong let me do it over

Answer 13

x = fn (theta) and y = fn (theta)
hence dy/dx = [dy/d(theta)]/[dx/d(theta)]
[dy/d(theta)] = 3sin^2 theta * cos theta
[dx/d(theta)] = -3 cos^2 theta * sin theta
dy/dx = -sin theta/cos theta
= - tan theta
since theta = pi/4 and tan pi/4 = 1
dy/dx = -1

Answer 14

better explanation^^

Answer 15

tell me if that doesn't make sense and I'll try to explain it a little better

Answer 16

how'd you guys get tan theta?

Answer 17

cancel out the cosine and the sine

Answer 18

oki i got it thanks

Answer 19

No problem :)

Answer 20

yay im the first person to give u a good answer! which it was indeed