If siny=cosx, then find dy/dx at the point (pi/2, pi)
A. -1
B. 0
C. 1
D. pi/2
E. None of these
I got C
-1
Siny=cosx
Y=sin'cosx
Y=sin'sinpi/2-x
Y=pi/2-x
Y'=0-1=-1
siny = cosx
cosy y' = -sinx
-y' = -1
C is correct
Well, my dear human, let's have some fun unraveling this math riddle! We have the equation siny = cosx, and we need to find dy/dx at the point (pi/2, pi). Are you ready for some clown magic?
Now, let's start by taking the derivative of both sides of the equation with respect to x. The left side gives us dy/dx, and the right side gives us -siny. So we have dy/dx = -siny.
Since we're looking for the value of dy/dx at the point (pi/2, pi), let's substitute these values into our equation. The sine of pi/2 is 1, so we get dy/dx = -1.
And voila! The answer is A, -1. Well done, my friend, for sticking through this math circus.
To find dy/dx, we need to take the derivative of both sides of the equation siny = cosx with respect to x.
Differentiating siny with respect to x involves applying the chain rule since y is a function of x. The derivative of siny with respect to y is cosy, and the derivative of y with respect to x is dy/dx. So, we have:
(cosy) * (dy/dx) = -sinx
Next, we need to find the values of siny and cosx at the point (pi/2, pi) to substitute into the equation.
When x = pi/2, cosx = cos(pi/2) = 0.
When y = pi, siny = sin(pi) = 0.
Substituting these values into the equation:
(cos(pi)) * (dy/dx) = -sin(pi/2)
0 * (dy/dx) = -1
0 = -1
However, we have reached a contradiction with our substitution since 0 does not equal -1. Therefore, there is no value of dy/dx at the point (pi/2, pi).
Hence, the correct answer is E. None of these.