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Please help, Simmons, page 579 problem 4. Prove that r1=theta and r2=1/theta intersect orthogonally at theta=1. Pt 1: they intersect, r = 1 = 1/1 which is true. Pt 2: Define psi1 as the angle between the line from the origin to a point on r=theta and the tangent to that point. tan(psi1) = r1/(dr1/dtheta) = theta/1 = theta. tan(psi2) = -theta orthonogal implies tan(psi1-psi2) = 1 (since psi2 is negative) this becomes: (tan(psi1)-tan(psi2))/(1+tan(psi1)tan(psi2)) = 1 2theta/(1-theta^2) = 1 using theta=1, 2/0 = 1, which is false what am i doing wrong here?

MIT 18.01 Single Variable Calculus (OCW)
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found out my mistake: tan(theta)=1 implies theta = 45 degrees, not 90

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