don steward
mathematics teaching 10 ~ 16

Monday, 31 July 2017

circle theorems meet 0.5absinC

an idea by Martin Wilson, in Harrogate, blending the circle theorems with area

you could use normal trigonometry (by bisecting chords) but Martin's intention is that students use the (more efficient) method of calculating 0.5 a b sinC

resources 2, 3 and 4 present an interesting relationship between sines
that is not easy to justify(?)
without involving the trig. formula sinA + sinB = 2sin(semi-sum).cos(semi-difference)
and noting that cosD = sin(90 - D)

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