solving 3 - 3sin(Ø) - 2cos^2(Ø) = 0 for Ø
- Thread starter LaurenK
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Use \(\displaystyle sin^{2}(\theta)\;+\;cos^{2}(\theta)\;=\;1\) to convert the cosine to sine. Then you have a quadratic in \(\displaystyle sin(\theta)\). You can use the quadratic formula, if all else fails.
\(\displaystyle sin(\theta)\;=\;???\)
\(\displaystyle sin(\theta)\;=\;???\)
skeeter
Elite Member
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pay attention to your signs ...
\(\displaystyle \L -2\sin^2{x} + 3\sin{x} - 1 = 0\)
\(\displaystyle \L 2\sin^2{x} - 3\sin{x} + 1 = 0\)
\(\displaystyle \L (2\sin{x} - 1)(\sin{x} - 1) = 0\)
... and good things happen to make life (and trig equations) much easier.
\(\displaystyle \L -2\sin^2{x} + 3\sin{x} - 1 = 0\)
\(\displaystyle \L 2\sin^2{x} - 3\sin{x} + 1 = 0\)
\(\displaystyle \L (2\sin{x} - 1)(\sin{x} - 1) = 0\)
... and good things happen to make life (and trig equations) much easier.