You can put this solution on YOUR website! Given;
(1) 4sin(2t) - 2tan(2t) = 0 or
(2) 4sin(2t) = 2tan(2t) or
(3) 2sin(2t) = tan(2t)
Since
(4) tan(x) = sin(x)/cos(x) we have
(5) 2sin(2t) = sin(2t)/cos(2t) or
(6) 2cos(2t) = 1 or
(7) cos(2t) = 1/2
Using the inverse of cosine we have
(8) 2t = arccos(1/2)
Use your scientific calculator to solve (8) for
(9) 2t = 60 or
(10) t = 30
Let's check this using (1).
Is (4sin(2*30) - 2tan(2*30) = 0)?
Is (4sin(60) - 2tan(60) = 0)?
Is (4*sqrt(3)/2 - 2*sqrt(3) = 0)?
Is (2*sqrt(3) - 2*sqrt(3) = 0)?
Is (0 = 0)? Yes
Answer: t = 30 degrees.
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