What is the general solution for 5sin^2(x)=cos(x) ?

The general solution for 5sin^2(x)=cos(x) is x=0.43944…+2pin,x=2pi-0.43944…+2pin

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5sin^2(x)=cos(x)

5 sin^{2} (x) = cos (x)

x = 0.43944 \dots + 2 πn, x = 2 π - 0.43944 \dots + 2 πn

Solution steps

5 sin^{2} (x) = cos (x)

Subtract

cos (x)

from both sides

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

Rewrite using trig identities

- cos (x) + (1 - cos^{2} (x)) \cdot 5 = 0

Solve by substitution

cos (x) = - \frac{1 + 101}{10}, cos (x) = \frac{101 - 1}{10}

cos (x) = - \frac{1 + 101}{10} :

No Solution

cos (x) = \frac{101 - 1}{10} : x = arccos (\frac{101 - 1}{10}) + 2 πn, x = 2 π - arccos (\frac{101 - 1}{10}) + 2 πn

Combine all the solutions

x = arccos (\frac{101 - 1}{10}) + 2 πn, x = 2 π - arccos (\frac{101 - 1}{10}) + 2 πn

Show solutions in decimal form

x = 0.43944 \dots + 2 πn, x = 2 π - 0.43944 \dots + 2 πn

cos (x) = \frac{1 + cos ( x )}{2}

cos (x) = \frac{1 + cos ( x )}{2}

sin (\frac{x}{2}) + \frac{3}{2} = 0

cos (x) = 0.818

sin (x) = \frac{150}{212.6} (sin (11 5^{\circ}))

What is the general solution for 5sin^2(x)=cos(x) ?
The general solution for 5sin^2(x)=cos(x) is x=0.43944…+2pin,x=2pi-0.43944…+2pin