SOLUTION: I really need help with this question Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y sin16x = x cos 2y, (π/2, π/4)

Algebra ->  Functions -> SOLUTION: I really need help with this question Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y sin16x = x cos 2y, (π/2, π/4)      Log On


   

Question 1154661: I really need help with this question
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
y sin16x = x cos 2y, (π/2, π/4)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
given: y+%2Asin%2816x%29+=+x+%2Acos%28+2y%29, (pi%2F2,+pi%2F4)

y+%2Asin+%2816x%29+=+x%2A+cos+%282y%29
16y+%2Acos%2816x%29++ y'sin%2816x%29+=+cos%282y%29+- 2xy'sin%282y%29

To find the slope m, replace y' with m, x with pi%2F2, and y+with pi%2F4.

4pi%2A+cos%288pi%29+%2B+m%2Asin%288pi%29+=+cos%28pi%2F2%29+-+pi%2Am%2Asin%28pi%2F2%29
4pi+%2A1+%2B+m%2A0+=+0+-+pi%2Am%2A1
4pi+=+-pi%2Am
m+=+-4
Equation of the tangent line:
y+-+pi%2F4+=+-4%28x+-+pi%2F2%29
y+=+-4x+%2B+2pi+%2B+pi%2F4
y+=+-4x+%2B+9pi%2F4