# Find every angle theta with 0 <= theta <= 2pi radians, and 2 sin^2(theta)+cos(theta)=2

Question
Find every angle theta with $$\displaystyle{0}\le\theta\le{2}\pi{r}{a}{d}{i}{a}{n}{s},{\quad\text{and}\quad}{2}{{\sin}^{{2}}{\left(\theta\right)}}+{\cos{{\left(\theta\right)}}}={2}$$

2021-02-26
$$\displaystyle{{\sin}^{{2}}=}{1}-{{\cos}^{{2}},}$$
so using x as $$\displaystyle\theta,{2}-{2}{{\cos}^{{2}}{x}}+{\cos{{x}}}={2},$$
$$\displaystyle{2}{{\cos}^{{2}}{x}}-{\cos{{x}}}={0},{\cos{{x}}}{\left({2}{\cos{{x}}}-{1}\right)}={0},$$
$$\displaystyle{\cos{{x}}}={0}{\quad\text{or}\quad}{0.5}$$
$$\displaystyle{x}=\frac{{\pi}}{{3}}{\quad\text{or}\quad}{60}°,\frac{{\pi}}{{2}}{\quad\text{or}\quad}{90}°,{3}\frac{{\pi}}{{2}}{\quad\text{or}\quad}{270}°,{5}\frac{{\pi}}{{3}}{\quad\text{or}\quad}{300}°.$$

### Relevant Questions

If $$\displaystyle{\cot{{\left(\theta\right)}}}={7}$$, what is $$\displaystyle{\sin{{\left(\theta\right)}}},{\cos{{\left(\theta\right)}}},{\sec{{\left(\theta\right)}}}$$ between 0 and $$\displaystyle{2}\pi$$?
Solve the equation $$\frac{\sin^{2}\theta/}{cos \theta}= \sec \theta-\cos \theta$$
Interval $$[0,2pi)$$
$$2 cos^2 x - cos x = 0$$?
Find an equation of the tangent line to the curve at the given point.
$$\displaystyle{y}={\sin{{\left({\sin{{x}}}\right)}}},{\left({2}\pi,{0}\right)}$$
If $$\cot \theta= -\sqrt{3} \ \text{and} \ sec \theta<0$$
Find $$\sin \theta$$
Prove that $$\displaystyle{\sec{{\left(\theta\right)}}}+{\csc{{\left(\theta\right)}}}={\left({\sin{{\left(\theta\right)}}}+{\cos{{\left(\theta\right)}}}\right)}{\left({\tan{{\left(\theta\right)}}}+{\cot{{\left(\theta\right)}}}\right)}$$
Solve the equation $$\sin \theta \cot \theta = \cos \theta$$
Solve the equation $$\frac{1}{\csc \theta-\cos \theta}=\frac{1+\cos \theta}{\sin \theta}$$
Solve the equation $$\frac{(2\sin \theta \sin 2\theta)}{\cos \theta+\cos 3\theta}=\tan (\theta) \tan(2\theta)$$
Solve the equation on the interval [0,2pi] $$\sin{{\left({x}+\frac{\pi}{{4}}\right)}}+ \sin{{\left({x}-\frac{\pi}{{4}}\right)}}={1}$$