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2006 SMT Team Round #13 - Compute $\cos\theta$

Source:

August 22, 2011
trigonometryconicshyperbolaanalytic geometrygraphing linesslope

Problem Statement

A ray is drawn from the origin tangent to the graph of the upper part of the hyperbola y2=x2−x+1y^2=x^2-x+1 in the first quadrant. This ray makes an angle of θ\theta with the positive xx-axis. Compute cos⁡θ\cos\theta.
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