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29

Part of 1994 AMC 12/AHSME

Problems(1)

1994 AMC 12 #29

Source:

12/30/2011
Points A,BA, B and CC on a circle of radius rr are situated so that AB=AC,AB>rAB=AC, AB>r, and the length of minor arc BCBC is rr. If angles are measured in radians, then AB/BC=AB/BC= [asy] draw(Circle((0,0), 13)); draw((-13,0)--(12,5)--(12,-5)--cycle); dot((-13,0)); dot((12,5)); dot((12,-5)); label("A", (-13,0), W); label("B", (12,5), NE); label("C", (12,-5), SE); [/asy] <spanclass=′latex−bold′>(A)</span> 12csc⁡14<spanclass=′latex−bold′>(B)</span> 2cos⁡12<spanclass=′latex−bold′>(C)</span> 4sin⁡12<spanclass=′latex−bold′>(D)</span> csc⁡12<spanclass=′latex−bold′>(E)</span> 2sec⁡12 <span class='latex-bold'>(A)</span>\ \frac{1}{2}\csc{\frac{1}{4}} \qquad<span class='latex-bold'>(B)</span>\ 2\cos{\frac{1}{2}} \qquad<span class='latex-bold'>(C)</span>\ 4\sin{\frac{1}{2}} \qquad<span class='latex-bold'>(D)</span>\ \csc{\frac{1}{2}} \qquad<span class='latex-bold'>(E)</span>\ 2\sec{\frac{1}{2}}
trigonometryAMC