cos(1/(4θ))=(-sqrt(2))/2

Solution

cos (\frac{1}{4 θ}) = \frac{- 2}{2}

θ = \frac{1}{π ( 3 + 8 n )}, θ = \frac{1}{π ( 5 + 8 n )}; n \neq = - \frac{3}{8}, n \neq = - \frac{5}{8}

Solution steps

cos (\frac{1}{4 θ}) = \frac{- 2}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

cos (\frac{1}{4 θ}) = - \frac{2}{2}

General solutions for

cos (\frac{1}{4 θ}) = - \frac{2}{2}

\frac{1}{4 θ} = \frac{3 π}{4} + 2 πn, \frac{1}{4 θ} = \frac{5 π}{4} + 2 πn

Solve

\frac{1}{4 θ} = \frac{3 π}{4} + 2 πn : θ = \frac{1}{π ( 3 + 8 n )}; n \neq = - \frac{3}{8}

Solve

\frac{1}{4 θ} = \frac{5 π}{4} + 2 πn : θ = \frac{1}{π ( 5 + 8 n )}; n \neq = - \frac{5}{8}

θ = \frac{1}{π ( 3 + 8 n )}, θ = \frac{1}{π ( 5 + 8 n )}; n \neq = - \frac{3}{8}, n \neq = - \frac{5}{8}

cos (x) tan (x) - 2 cos^{2} (x) = - 1

3 cot (\frac{1}{4} x) = 1

2 sin (\frac{π}{4} - x) + 3 = 0

3.1 = 48.1 (1 - cos (\frac{28.66 x}{48.1}))

sin^{2} (x) - 2 cos (x) = - 2