What is the general solution for cos(θ)=(sqrt(3))/2 ,sin(θ) ?

The general solution for cos(θ)=(sqrt(3))/2 ,sin(θ) is No Solution for θ\in\mathbb{R}

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cos(θ)=(sqrt(3))/2 ,sin(θ)

cos (θ) = \frac{3}{2}, sin (θ)

No Solution for θ \in R

Solution steps

cos (θ) = \frac{3}{2}, sin (θ)

General solutions for

cos (θ) = \frac{3}{2}

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Solutions for the range

sin (θ)

No Solution for θ \in R

sin (θ) = 0.788

arctan (θ) = - 3

cos (θ) = \frac{2}{6}

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

\frac{tan ( x ) ( - tan ^{2} ( x ) + 3 )}{1 - tan ^{2} ( x )} = 0

What is the general solution for cos(θ)=(sqrt(3))/2 ,sin(θ) ?
The general solution for cos(θ)=(sqrt(3))/2 ,sin(θ) is No Solution for θ\in\mathbb{R}