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

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

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cos(x)=(sqrt(3))/2 ,tan(x)

cos (x) = \frac{3}{2}, tan (x)

No Solution for x \in R

Solution steps

cos (x) = \frac{3}{2}, tan (x)

General solutions for

cos (x) = \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}

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

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

Solutions for the range

tan (x)

No Solution for x \in R

tan (t) = \frac{7}{24}

cos (x) = 0.59

cos (x) = 0.92

cos (x) = 0.94

cos (x) = 0.73

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