What is the general solution for 1-cos^2(θ)-6959cos(θ)=0 ?

The general solution for 1-cos^2(θ)-6959cos(θ)=0 is θ=1.57065…+2pin,θ=2pi-1.57065…+2pin

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1-cos^2(θ)-6959cos(θ)=0

1 - cos^{2} (θ) - 6959 cos (θ) = 0

θ = 1.57065 \dots + 2 πn, θ = 2 π - 1.57065 \dots + 2 πn

Solution steps

1 - cos^{2} (θ) - 6959 cos (θ) = 0

Solve by substitution

cos (θ) = - \frac{6959 + 48427685}{2}, cos (θ) = \frac{48427685 - 6959}{2}

cos (θ) = - \frac{6959 + 48427685}{2} :

No Solution

cos (θ) = \frac{48427685 - 6959}{2} : θ = arccos (\frac{48427685 - 6959}{2}) + 2 πn, θ = 2 π - arccos (\frac{48427685 - 6959}{2}) + 2 πn

Combine all the solutions

θ = arccos (\frac{48427685 - 6959}{2}) + 2 πn, θ = 2 π - arccos (\frac{48427685 - 6959}{2}) + 2 πn

Show solutions in decimal form

θ = 1.57065 \dots + 2 πn, θ = 2 π - 1.57065 \dots + 2 πn

(\frac{0.87 \cdot 1.04 \cdot sin ( 2 0 ^{\circ} - x )}{0.4}) = 0.05

sin (y) = 0, x cos (y) = 0

sin (6 0^{\circ} - x) - sin (6 0^{\circ} + x) = \frac{3}{2}

tan (\frac{x}{4}) + 3 = 0, 0 \leq x \leq 2 π

cot^{(2)} (x) - csc (x) - 1 = 0

What is the general solution for 1-cos^2(θ)-6959cos(θ)=0 ?
The general solution for 1-cos^2(θ)-6959cos(θ)=0 is θ=1.57065…+2pin,θ=2pi-1.57065…+2pin