What is the general solution for cos^2(θ)+(5^2cos(θ))/(9.81(8))-1=0 ?

The general solution for cos^2(θ)+(5^2cos(θ))/(9.81(8))-1=0 is θ=0.54845…+2pin,θ=2pi-0.54845…+2pin

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cos^2(θ)+(5^2cos(θ))/(9.81(8))-1=0

cos^{2} (θ) + \frac{5 ^{2} cos ( θ )}{9.81 ( 8 )} - 1 = 0

θ = 0.54845 \dots + 2 πn, θ = 2 π - 0.54845 \dots + 2 πn

Solution steps

cos^{2} (θ) + \frac{5 ^{2} cos ( θ )}{9.81 ( 8 )} - 1 = 0

Solve by substitution

cos (θ) = \frac{- 25 + 25261.4416}{156.96}, cos (θ) = \frac{- 25 - 25261.4416}{156.96}

cos (θ) = \frac{- 25 + 25261.4416}{156.96} : θ = arccos (\frac{- 25 + 25261.4416}{156.96}) + 2 πn, θ = 2 π - arccos (\frac{- 25 + 25261.4416}{156.96}) + 2 πn

cos (θ) = \frac{- 25 - 25261.4416}{156.96} :

No Solution

Combine all the solutions

θ = arccos (\frac{- 25 + 25261.4416}{156.96}) + 2 πn, θ = 2 π - arccos (\frac{- 25 + 25261.4416}{156.96}) + 2 πn

Show solutions in decimal form

θ = 0.54845 \dots + 2 πn, θ = 2 π - 0.54845 \dots + 2 πn

105 = 100 + 30 sin (\frac{12 π}{5} t)

\frac{3}{sin ( x )} = \frac{1}{cos ( x )}

2 cos (t) - 2 sin (2 t) = 0

4 sin (x) = - 2 cos (x)

3 sin (2 x) = 1.5

What is the general solution for cos^2(θ)+(5^2cos(θ))/(9.81(8))-1=0 ?
The general solution for cos^2(θ)+(5^2cos(θ))/(9.81(8))-1=0 is θ=0.54845…+2pin,θ=2pi-0.54845…+2pin