Hi
Find all exact solutions on [0,2pi)
2(cos^2)x + 3sinx = 3
Someone said i had to use (cos^2)x + (sin^2)x = 1 and use sin x as a variable, but i do not understand what that means.
Can someone explain to me step by step?
Hi
Find all exact solutions on [0,2pi)
2(cos^2)x + 3sinx = 3
Someone said i had to use (cos^2)x + (sin^2)x = 1 and use sin x as a variable, but i do not understand what that means.
Can someone explain to me step by step?
Exactly what that person said. Use sin x as a variable.
Replace $\displaystyle \cos^2 x$ with $\displaystyle 1 - \sin^2 x$:
$\displaystyle \begin{aligned}
2\cos^2 x + 3\sin x &= 3 \\
2(1 - \sin^2 x) + 3\sin x &= 3 \\
2 - 2\sin^2 x + 3\sin x &= 3 \\
2\sin^2 x - 3\sin x + 1 &= 0
\end{aligned}$
See how this looks like a quadratic? If you replaced $\displaystyle \sin x$ with $\displaystyle y$ you would get
$\displaystyle 2y^2 - 3y + 1 = 0$
Solve the quadratic for y, plug back in $\displaystyle \sin x$ for y, and solve for x.