Question

4. Solve the equation on the interval [0,2pi)
4sin^2(x)-3=0
5. Solve the equation on the interval [0,2pi)
cos(3x)=-1
6. Solve the equation for theta , giving a general formula for all of the solutions: tan theta=-1
I got 3pi/4+pin but i think theres more??

Answer 1

\[4 \sin ^2x=3,2\sin ^2x=\frac{ 3 }{ 2 },1-\cos 2x=\frac{ 3 }{ 2 },\cos 2x=1-\frac{ 3 }{ 2 }=-\frac{ 1 }{ 2 }\]
\[=-\cos \frac{ \pi }{ 3 }=\cos \left( \pi-\frac{ \pi }{ 3 } \right),\cos \left( \pi+\frac{ \pi }{ 3 } \right)=\cos \left( 2n \pi+\frac{ 2 \pi }{ 3 } \right),\cos \left( 2n \pi+\frac{ 4 \pi }{ 3 } \right)\]
where n is an integer.
2x=?
x=?