Find the equation of the tangent to the unit circle when x=sqrt(3)/2 (in the first quadrant)
Unit circle: x2 + y2 = 1 when x = sqrt(3)/2: y2 = 1 - (sqrt(3)/2)2 y2 = 1 - 3/4 y2 = 1/4 y = 1/2 or -1/2 (first quadrant, so y is positive, i.e. y = 1/2) find gradient at (sqrt(3)/2, 1/2): x2 + y2 = 1 2x + 2y dy/dx = 0 dy/dx = -2x/2y dy/dx = -x/y Substitute x= sqrt(3)/2, y = 1/2 dy/dx = -sqrt(3) Find equation of line: y - y1 = m(x - x1) y - 1/2 = -sqrt(3)(x-sqrt(3)/2) y = -sqrt(3)x + 3/2 + 1/2 y = -sqrt(3)x + 2
KJ
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