2sin^2theta +3cos theta =0
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Do I have to find all the solutions or values where the theta on a graph equals zero?
Can somebody help me
2 (1 - cos^2 x) - 3 cos x = 0
2 - 2 cos^2 x - 3 cos x = 0
Now we have a standard quadratic equation in "cos x".
Let c = cos x.
2 c^2 + 3c - 2 = 0
(2c - 1) (c + 2) = 0
c = 1/2 or -2
-2 is out of the running, as cos x is always between 0 and 1.
So we have cos x = 1/2
That corresponds to pi / 3 (60°) or 5 pi / 3 (300°). << Answer
To check our answer:
The sin of either of those angles is ± sqrt(3) / 2,
and sin^2 x = 3/4 in both cases,
so 2 sin^2 x = 3/2.
3 * cos x = 3/2, so we have 2 sin^2 x - 3 cos x = 0, as required.
Can somebody help me
2 (1 - cos^2 x) - 3 cos x = 0
2 - 2 cos^2 x - 3 cos x = 0
Now we have a standard quadratic equation in "cos x".
Let c = cos x.
2 c^2 + 3c - 2 = 0
(2c - 1) (c + 2) = 0
c = 1/2 or -2
-2 is out of the running, as cos x is always between 0 and 1.
So we have cos x = 1/2
That corresponds to pi / 3 (60°) or 5 pi / 3 (300°). << Answer
To check our answer:
The sin of either of those angles is ± sqrt(3) / 2,
and sin^2 x = 3/4 in both cases,
so 2 sin^2 x = 3/2.
3 * cos x = 3/2, so we have 2 sin^2 x - 3 cos x = 0, as required.
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