Given (sin theta = frac{sqrt{3}}{2}, 0° leq theta leq 90°), find (tan 2theta) in surd form.
-
A.
(- sqrt{3}) -
B.
(-frac{sqrt{3}}{2}) -
C.
(frac{sqrt{3}}{2}) -
D.
(sqrt{3})
Correct Answer: Option A
Explanation
(sin theta = frac{sqrt{3}}{2} implies opp = sqrt{3}; hyp = 2)
(adj^{2} = 2^{2} – (sqrt{3})^{2} = 1 implies adj = 1)
(cos theta = frac{1}{2})
(sin 2theta = sin (180 – theta) = sin theta = frac{sqrt{3}}{2})
(cos 2theta = cos (180 – theta) = -cos theta = -frac{1}{2})
(tan 2theta = frac{sin 2theta}{cos 2theta} = frac{frac{sqrt{3}}{2}}{-frac{1}{2}})
= (- sqrt{3})