What is the general solution for 4cos^2(x)=5+4sin(x),(0,2pi) ?

The general solution for 4cos^2(x)=5+4sin(x),(0,2pi) is x=(7pi)/6 ,x=(11pi)/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4cos^2(x)=5+4sin(x),(0,2pi)

4 cos^{2} (x) = 5 + 4 sin (x), (0, 2 π)

x = \frac{7 π}{6}, x = \frac{11 π}{6}

Solution steps

4 cos^{2} (x) = 5 + 4 sin (x), (0, 2 π)

Subtract

5 + 4 sin (x)

from both sides

4 cos^{2} (x) - 5 - 4 sin (x) = 0

Rewrite using trig identities

- 1 - 4 sin (x) - 4 sin^{2} (x) = 0

Solve by substitution

sin (x) = - \frac{1}{2}

sin (x) = - \frac{1}{2}, (0, 2 π) : x = \frac{7 π}{6}, x = \frac{11 π}{6}

Combine all the solutions

x = \frac{7 π}{6}, x = \frac{11 π}{6}

\frac{sin ( S )}{53} = \frac{sin ( 11 5 ^{\circ} )}{83}

25 sin^{2} (x) - 10 sin (x) + 1 = 0

4 - 4 sin (θ) = 2

1 - 2 cos (x) = sin^{2} (x)

cos (x) = \frac{84}{98}

What is the general solution for 4cos^2(x)=5+4sin(x),(0,2pi) ?
The general solution for 4cos^2(x)=5+4sin(x),(0,2pi) is x=(7pi)/6 ,x=(11pi)/6