sec(3x)= 2/(sqrt(3)),0<= x<= 2pi

Solution

sec (3 x) = \frac{2}{3}, 0 \leq x \leq 2 π

x = \frac{π}{18}, x = \frac{11 π}{18}, x = \frac{13 π}{18}, x = \frac{23 π}{18}, x = \frac{25 π}{18}, x = \frac{35 π}{18}

Solution steps

sec (3 x) = \frac{2}{3}, 0 \leq x \leq 2 π

Simplify

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

General solutions for

sec (3 x) = \frac{2 3}{3}

3 x = \frac{π}{6} + 2 πn, 3 x = \frac{11 π}{6} + 2 πn

Solve

3 x = \frac{π}{6} + 2 πn : x = \frac{π}{18} + \frac{2 πn}{3}

Solve

3 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{18} + \frac{2 πn}{3}

x = \frac{π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

Solutions for the range

0 \leq x \leq 2 π

x = \frac{π}{18}, x = \frac{11 π}{18}, x = \frac{13 π}{18}, x = \frac{23 π}{18}, x = \frac{25 π}{18}, x = \frac{35 π}{18}

sec (4 x) - 2 = 0

2 cos (θ) sin (θ) = cos (θ)

- 2 sin (x) = 0

sin (3 x) = \frac{3}{2}

cos^{3} (x) = 0