SOLUTION: Sin^4 2theta -2 sin^2 2theta = -1
(3tan 3theta)^2-27=0
Solve for theta. Solutions should have exact radian measures such that 0<theta<2pi.
(< is equal to or greater than)
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Question 1125838: Sin^4 2theta -2 sin^2 2theta = -1
(3tan 3theta)^2-27=0
Solve for theta. Solutions should have exact radian measures such that 0
(< is equal to or greater than)
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
First equation....
or
0 < x < 2pi --> 0 < 2x < 4pi
On (0,4pi), sin(x) is 1 or -1 at pi/2, 3pi/2, 5pi/2, and 7pi/2.
On (0,2pi), sin(2x) is 1 or -1 at pi/2, 3pi/2, 5pi/2, and 7pi/2.
So the solution set for this equation, for x on (0,2pi), is
{pi/4, 3pi/4, 5pi/4, 7pi/4}
Second equation....
or
0 < x < 2pi --> 0 < 3x < 6pi
On (0,6pi), tan(x) is sqrt(3) or -sqrt(3) at pi/3, 2pi/3, 4pi/3, 5pi/3, 7pi/3, 8pi/3, 10pi/3, 11pi/3, 13pi/3, 14pi/3, 16pi/3, and 17pi/3.
On (0,2pi), tan(3x) is sqrt(3) or -sqrt(3) at pi/9, 2pi/9, 4pi/9, 5pi/9, 7pi/9, 8pi/9, 10pi/9, 11pi/9, 13pi/9, 14pi/9, 16pi/9, and 17pi/9.
So the solution set for this equation, for x on (0,2pi), is
{pi/9, 2pi/9, 4pi/9, 5pi/9, 7pi/9, 8pi/9, 10pi/9, 11pi/9, 13pi/9, 14pi/9, 16pi/9, 17pi/9}
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