Find the maximum angle X in the range 0^{\circ} \leq

Maximus George 2022-01-24 Answered
Find the maximum angle X in the range 0x360 which satisfies the equation cos2(2x)+3sin(2x)74=0
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Expert Answer

basgrwthej
Answered 2022-01-25 Author has 13 answers
Note you have cos22x=1sin22x; with sin2x=t you get
1t2+t374=0
so the equation can be rewritten
4t24t3+3=0
This is actually (2t3)2=0, so the only root is t=32. Hence 2x=π3+2kπ  or  2x=2π3+2kπ. Hence
x=π6+kπ  or  x=π3+kπ
If you prefer degrees,
x=30+k180  or  x=60+k180
It shouldn't be difficult to find the maximum solution.
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