What is the general solution for 1/3 cos(θ)=-(sqrt(3))/6 ?

The general solution for 1/3 cos(θ)=-(sqrt(3))/6 is θ=(5pi)/6+2pin,θ=(7pi)/6+2pin

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1/3 cos(θ)=-(sqrt(3))/6

\frac{1}{3} cos (θ) = - \frac{3}{6}

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

Degrees

θ = 15 0^{\circ} + 36 0^{\circ} n, θ = 21 0^{\circ} + 36 0^{\circ} n

Solution steps

\frac{1}{3} cos (θ) = - \frac{3}{6}

Multiply both sides by

3

\frac{1}{3} cos (θ) = - \frac{3}{6}

Multiply both sides by

3

3 \cdot \frac{1}{3} cos (θ) = 3 (- \frac{3}{6})

Simplify

3 \cdot \frac{1}{3} cos (θ) = 3 (- \frac{3}{6})

Simplify

3 \cdot \frac{1}{3} cos (θ) : cos (θ)

3 \cdot \frac{1}{3} cos (θ)

Multiply fractions:

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

= \frac{1 \cdot 3}{3} cos (θ)

Cancel the common factor:

3

= cos (θ) \cdot 1

Multiply:

cos (θ) \cdot 1 = cos (θ)

= cos (θ)

Simplify

3 (- \frac{3}{6}) : - \frac{3}{2}

3 (- \frac{3}{6})

Remove parentheses:

(- a) = - a

= - 3 \cdot \frac{3}{6}

Multiply fractions:

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

= - \frac{3 \cdot 3}{6}

Cancel the common factor:

3

= - \frac{3}{2}

cos (θ) = - \frac{3}{2}

cos (θ) = - \frac{3}{2}

cos (θ) = - \frac{3}{2}

General solutions for

cos (θ) = - \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}

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

sin (\frac{x}{2}) + cos (\frac{x}{2}) = 1

cos (2 x) = 3 sin (2 x)

3 sin (2 x - 1 5^{\circ}) = cos (2 x - 1 5^{\circ})

sec (\frac{x}{2}) - 2 = 0

sin (x) = \frac{12}{20}

What is the general solution for 1/3 cos(θ)=-(sqrt(3))/6 ?
The general solution for 1/3 cos(θ)=-(sqrt(3))/6 is θ=(5pi)/6+2pin,θ=(7pi)/6+2pin