Question 1156517: Please help me to answer this! Thank you :
5 + 2cos x - 8sin^2 x = 0 Found 2 solutions by Theo, josmiceli:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! start with 5 + 2 * cos(x) - 8 * sin^2(x) = 0
since sin^2(x) + cos^2(x) = 1, then sdin^2(x) = 1 - cos^2(x).
replace sin^2(x) with that to get:
5 + 2 * cos(x) - 8 * (1 - cos^2(x)) = 0
simplify to get:
5 + 2 * cos(x) - 8 + 8 * cos^2(x) = 0
order the equation in descending order of degree and combine like terms to get:
8 * cos^2(x) + 2 * cos(x) - 3 = 0
factor this quadratic equation to get:
cos(x) = -.75 or .5
assume these are both positive and solve for x in the first quadrant to get:
x = 41.40962211 degrees or x = 60 degrees.
cosine = -.75 is negative which means the angle has to be in the second and third quadrant.
x = 180 - 41.40962211 in the second quadrant = 138.5903779 degrees.
x = 180 + 41.40962211 in the third quadrant = 221.4096221 degrees.
cosine = .5 is positive which means the angle has to be in the first and fourth quadrant.
x = 60 degrees in the first quadrant.
x = 360 - 60 = 300 degrees in the fourth quadrant.
your angle can be 60, 138.5903779, 221.4096221, and 300 degrees.
this is confirmed by the graph of the equation shown below.
You can put this solution on YOUR website!
Use identity:
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Let
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Use quadratic formula:
and
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and
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and
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My answers are:
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I'll check one of the answers. You can check the rest
Looks OK
To convert back to degrees, multiply answers by
Definitely get a 2nd opinion if needed
and check my math
