What is the general solution for cos(θ)= 4/7 ,tan(θ)<0 ?

The general solution for cos(θ)= 4/7 ,tan(θ)<0 is No Solution for θ\in\mathbb{R}

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cos(θ)= 4/7 ,tan(θ)<0

cos (θ) = \frac{4}{7}, tan (θ) < 0

No Solution for θ \in R

Solution steps

cos (θ) = \frac{4}{7}, tan (θ) < 0

Apply trig inverse properties

cos (θ) = \frac{4}{7}

General solutions for

cos (θ) = \frac{4}{7}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

θ = arccos (\frac{4}{7}) + 2 πn, θ = 2 π - arccos (\frac{4}{7}) + 2 πn

θ = arccos (\frac{4}{7}) + 2 πn, θ = 2 π - arccos (\frac{4}{7}) + 2 πn

Solutions for the range

tan (θ) < 0

No Solution for θ \in R

tan (θ) = \frac{4}{2}

e^{s i n (x)} - e^{- s i n (x)} = 2

cos (x) \cdot sec (x) \cdot cot^{2} (x) = csc^{2} (x)

2 sin (3 x) + 2 sin (x) = 0

(cos (x) - 1) (3 cot (x) + 1) = 0

What is the general solution for cos(θ)= 4/7 ,tan(θ)<0 ?
The general solution for cos(θ)= 4/7 ,tan(θ)<0 is No Solution for θ\in\mathbb{R}