Math  /  Calculus

QuestionEXAMPLE 2.7.4 Find an equation of the tangent line to the graph of the curve sin1x+sin1y=π2\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{2} at the point P(22,22)P\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right).

Studdy Solution
Use the point-slope form of the equation of a line, yy1=m(xx1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is the point of tangency:
y22=1(x22)y - \frac{\sqrt{2}}{2} = -1\left(x - \frac{\sqrt{2}}{2}\right)
Simplify to get the equation of the tangent line:
y22=x+22y - \frac{\sqrt{2}}{2} = -x + \frac{\sqrt{2}}{2}
y=x+22+22y = -x + \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}
y=x+2y = -x + \sqrt{2}
The equation of the tangent line is:
y=x+2 y = -x + \sqrt{2}

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