8. a) Find the differential dy of y = cos x
b) Evaluate dy for the given values of x and dx. (Round your answer to three decimal places.) x = 𝜋/3 and dx = −0.01.
for a), i got dy = - sin(x) . dx, which is correct, but I'm having issue with b). I keep getting 1.83 x 10^-4, which cannot be entered into the software, so i am really confused
This is very weird. Not sure how to help you since 1.83*10^-4 is 0.000183 as a decimal
Ah, I see where the OP went wrong. The correct answer is supposed to be 0.009 since -sin(π/3) * -0.01 = 0.00866 ≈ 0.009
@oobleck looks like you forgot to make the differential negative
You have to be in RADIANS, not degrees
I just asked my teacher what to do, since i have the right answer it just won't be accepted
dy = -sin(x) dx
(b) -sin(π/3) * 0.01 = -0.00866
how did you get your result?
To evaluate dy for the given values of x and dx, we can use the formula dy = -sin(x) * dx.
For x = 𝜋/3 and dx = -0.01:
First, substitute the value of x into the equation dy = -sin(x) * dx:
dy = -sin(𝜋/3) * (-0.01)
Next, calculate the value of sin(𝜋/3):
sin(𝜋/3) = √3/2
Substitute the value of sin(𝜋/3) into the equation:
dy = -(√3/2) * (-0.01)
Multiply the numbers:
dy = (√3/2) * 0.01
Finally, calculate the result:
dy = 0.01 * (√3/2)
To round your answer to three decimal places, evaluate the expression:
dy ≈ 0.01 * 0.866 ≈ 0.00866
Therefore, the evaluated value of dy for x = 𝜋/3 and dx = -0.01 is approximately 0.00866.