Examples of Math Problems: if tan(theta) = -3 and cos(theta) < 0, then tan(theta/2) = ?

Friday, May 29, 2015

if tan(theta) = -3 and cos(theta) < 0, then tan(theta/2) = ?

tan%28theta%29=opp%2Fadj=-3%2F1

so

hyp=sqrt%281%5E2%2B%28-3%29%5E2%29=sqrt%2810%29

so

sin%28theta%29=%283%2Asqrt%2810%29%29%2F10

cos%28theta%29=-sqrt%2810%29%2F10

(we take the negative case because cosine is negative for this example)
now
tan%28theta%2F2%29=sin%28theta%29%2F%281%2Bcos%28theta%29%29

tan%28theta%2F2%29=sin%28theta%29%2F%281%2Bcos%28theta%29%29

Therefore...

tan%28theta%2F2%29=%28%283%2Asqrt%2810%29%29%2F10%29%2F%281-sqrt%2810%29%2F10%29

tan%28theta%2F2%29=%28%283%2Asqrt%2810%29%29%2F10%29%2F%281-sqrt%2810%29%2F10%29

which simplifies to
%28sqrt%2810%29%2B1%29%2F3

%28sqrt%2810%29%2B1%29%2F3

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