find sin theta and  theta if tangent theta is 1/2
asked Nov 13, 2016 in Trigonometry Answers by anonymous

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Let t represent theta. Assume t<90º.

tan(t)=1/2=opposite/adjacent. Hypotenuse=√(opposite^2+adjacent^2)=√5.

sin(t)=opposite/hypotenuse=1/√5 which can also be written rationally as √5/5=0.4472 approx.

cos(t)=adjacent/hypotenuse=2/√5=2√5/5=0.8944 approx.

t=arctan(1/2)=26.565º; t=arcsin(√5/5)=26.565º (approx).

If cos(t)=1/2 t=60º, opposite=√(4-1)=√3. tan(t)=√3=1.732; sin(t)=√3/2=0.866 approx.

answered Nov 13, 2016 by Rod Top Rated User (416,580 points)
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