What is the general solution for 8sqrt(2)cos(θ)+6=-2 ?

The general solution for 8sqrt(2)cos(θ)+6=-2 is θ=(3pi)/4+2pin,θ=(5pi)/4+2pin

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Popular Trigonometry >

8sqrt(2)cos(θ)+6=-2

Solution

82 cos (θ) + 6 = - 2

Solution

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

Degrees

θ = 13 5^{\circ} + 36 0^{\circ} n, θ = 22 5^{\circ} + 36 0^{\circ} n

Solution steps

82 cos (θ) + 6 = - 2

Move

6

to the right side

82 cos (θ) + 6 = - 2

Subtract

6

from both sides

82 cos (θ) + 6 - 6 = - 2 - 6

Simplify

82 cos (θ) = - 8

82 cos (θ) = - 8

Divide both sides by

82

82 cos (θ) = - 8

Divide both sides by

82

\frac{8 2 cos ( θ )}{8 2} = \frac{- 8}{8 2}

Simplify

\frac{8 2 cos ( θ )}{8 2} = \frac{- 8}{8 2}

Simplify

\frac{8 2 cos ( θ )}{8 2} : cos (θ)

\frac{8 2 cos ( θ )}{8 2}

Divide the numbers:

\frac{8}{8} = 1

= \frac{2 cos ( θ )}{2}

Cancel the common factor:

2

= cos (θ)

Simplify

\frac{- 8}{8 2} : - \frac{2}{2}

\frac{- 8}{8 2}

Apply the fraction rule:

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

= - \frac{8}{8 2}

Divide the numbers:

\frac{8}{8} = 1

= - \frac{1}{2}

Rationalize

- \frac{1}{2} : - \frac{2}{2}

- \frac{1}{2}

Multiply by the conjugate

\frac{2}{2}

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

1 \cdot 2 = 2

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= - \frac{2}{2}

= - \frac{2}{2}

cos (θ) = - \frac{2}{2}

cos (θ) = - \frac{2}{2}

cos (θ) = - \frac{2}{2}

General solutions for

cos (θ) = - \frac{2}{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{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

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

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 8sqrt(2)cos(θ)+6=-2 ?
The general solution for 8sqrt(2)cos(θ)+6=-2 is θ=(3pi)/4+2pin,θ=(5pi)/4+2pin