cos(4x)=-1/2 ,0<= x<= 2pi

Solution

cos (4 x) = - \frac{1}{2}, 0 \leq x \leq 2 π

x = \frac{π}{6}, x = \frac{π}{3}, x = \frac{2 π}{3}, x = \frac{5 π}{6}, x = \frac{7 π}{6}, x = \frac{4 π}{3}, x = \frac{5 π}{3}, x = \frac{11 π}{6}

Solution steps

cos (4 x) = - \frac{1}{2}, 0 \leq x \leq 2 π

General solutions for

cos (4 x) = - \frac{1}{2}

4 x = \frac{2 π}{3} + 2 πn, 4 x = \frac{4 π}{3} + 2 πn

Solve

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

Solve

4 x = \frac{4 π}{3} + 2 πn : x = \frac{π}{3} + \frac{πn}{2}

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

Solutions for the range

0 \leq x \leq 2 π

x = \frac{π}{6}, x = \frac{π}{3}, x = \frac{2 π}{3}, x = \frac{5 π}{6}, x = \frac{7 π}{6}, x = \frac{4 π}{3}, x = \frac{5 π}{3}, x = \frac{11 π}{6}

3 csc^{2} (x) + 1.5 cot (x) = 15

sin (y) = cos (y)

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

θ, 2 cos^{2} (θ) + 9 cos (θ) - 5 = 0

tan (3 x) = - 3, 0 \leq x \leq 2 π