What is the general solution for tan(x)=((sqrt(3))/2)/(1/2) ?

The general solution for tan(x)=((sqrt(3))/2)/(1/2) is x= pi/3+pin

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tan(x)=((sqrt(3))/2)/(1/2)

tan (x) = \frac{\frac{3}{2}}{\frac{1}{2}}

x = \frac{π}{3} + πn

Solution steps

tan (x) = \frac{\frac{3}{2}}{\frac{1}{2}}

Simplify

\frac{\frac{3}{2}}{\frac{1}{2}} : 3

\frac{\frac{3}{2}}{\frac{1}{2}}

Divide fractions:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{3 \cdot 2}{2 \cdot 1}

Refine

= \frac{3 \cdot 2}{2}

Cancel the common factor:

2

= 3

General solutions for

tan (x) = 3

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{3} + πn

x = \frac{π}{3} + πn

tan (2 x) + sec (2 x) = 11

- 8 sin (x) + 8 cos (2 x) = 0

tan^{2} (x) + 2 sec (x) + 2 = 0

sin (θ) = 1 + cos (θ)

7 cos (2 x) = 7 cos^{2} (x) - 3

What is the general solution for tan(x)=((sqrt(3))/2)/(1/2) ?
The general solution for tan(x)=((sqrt(3))/2)/(1/2) is x= pi/3+pin