Find the curvature K of the curve. r(t) = 5 cos(πt)i + sin(πt)j
Added by John A.
Step 1
r(t) = 5cos(πt)i + sin(πt)j r'(t) = -5πsin(πt)i + πcos(πt)j r''(t) = -5π^2cos(πt)i - π^2sin(πt)j Now, we need to find the magnitudes of r'(t) and r''(t). |r'(t)| = √((-5πsin(πt))^2 + (πcos(πt))^2) = √(25π^2sin^2(πt) + π^2cos^2(πt)) |r''(t)| = Show more…
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