What is the general solution for sec(θ)=3,sin(θ)<0 ?

The general solution for sec(θ)=3,sin(θ)<0 is No Solution for θ\in\mathbb{R}

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sec(θ)=3,sin(θ)<0

sec (θ) = 3, sin (θ) < 0

No Solution for θ \in R

Solution steps

sec (θ) = 3, sin (θ) < 0

Apply trig inverse properties

θ = arcsec (3) + 2 πn, θ = 2 π - arcsec (3) + 2 πn

Solutions for the range

sin (θ) < 0

No Solution for θ \in R

cos (x) tan (x) - cos (x) = 0, 0 \leq x \leq 2 π

sin^{2} (2 θ) - 5 sin (2 θ) - 1 = 0

- \frac{π}{30} sin (\frac{π}{90} (x + 20)) = 0

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

cos (x) = - \frac{22}{7.28 \cdot 20}

What is the general solution for sec(θ)=3,sin(θ)<0 ?
The general solution for sec(θ)=3,sin(θ)<0 is No Solution for θ\in\mathbb{R}