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## Homework Statement

Find an equation for the line tangent to the curve at the point defined by the given value of t.

x = 2 cos t

y = 2 sin t

t = pi/4

## Homework Equations

sin (pi/4) = sqrt(2)/2

cos (pi/4) = sqrt(2)/2

## The Attempt at a Solution

Determining the slope:

[dy/dt]/[dx/dt] = [2 cos t]/[-2 sin t]

= [2 cos (pi/4)]/[-2 sin (pi/4)]

= [2 (sqrt(2)/2)]/[-2 (sqrt(2)/2)]

= [sqrt(2)]/[-sqrt(2)]

= -1

slope = -1

Finding the line:

y = mx+b

m = -1

2 sin t = -1(2 cos t)+ b

2 sin t = -2 cos t + b

2 sin (pi/4) = -2 cos(pi/4) + b

2 [sqrt(2)/2] = -2 [sqrt(2)/2] + b

sqrt(2) = -sqrt(2) + b

b = 2 sqrt(2)

y = -1x + 2 sqrt(2)

The answer the book has says [y = -x + 2]. I'm not sure what I did wrong with the problem.