Find an equation of the line tangent to the curve at the point corresponding to the given value of \( t \). \[ \mathrm{x}=\cos \mathrm{t}+\mathrm{t} \sin \mathrm{t}, \mathrm{y}=\sin \mathrm{t}-\mathrm{t} \cos \mathrm{t} ; \mathrm{t}=\frac{\pi}{4} \]
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- Calculate \( x \): \[ x = \cos\left(\frac{\pi}{4}\right) + \frac{\pi}{4} \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} + \frac{\pi}{4} \cdot \frac{\sqrt{2}}{2} \] - Calculate \( y \): \[ y = \sin\left(\frac{\pi}{4}\right) - \frac{\pi}{4} Show more…
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