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Popular >

-8cos(-4θ+150)=4sqrt(3)

Solution

- 8 cos (- 4 θ + 150) = 43

Solution

θ = \frac{75}{2} - \frac{5 π}{24} - \frac{πn}{2}, θ = \frac{75}{2} - \frac{7 π}{24} - \frac{πn}{2}

Degrees

θ = 2111.09173 \dots^{\circ} - 9 0^{\circ} n, θ = 2096.09173 \dots^{\circ} - 9 0^{\circ} n

Solution steps

- 8 cos (- 4 θ + 150) = 43

Divide both sides by

- 8

- 8 cos (- 4 θ + 150) = 43

Divide both sides by

- 8

\frac{- 8 cos ( - 4 θ + 150 )}{- 8} = \frac{4 3}{- 8}

Simplify

\frac{- 8 cos ( - 4 θ + 150 )}{- 8} = \frac{4 3}{- 8}

Simplify

\frac{- 8 cos ( - 4 θ + 150 )}{- 8} : cos (- 4 θ + 150)

\frac{- 8 cos ( - 4 θ + 150 )}{- 8}

Apply the fraction rule:

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

= \frac{8 cos ( - 4 θ + 150 )}{8}

Divide the numbers:

\frac{8}{8} = 1

= cos (- 4 θ + 150)

Simplify

\frac{4 3}{- 8} : - \frac{3}{2}

\frac{4 3}{- 8}

Apply the fraction rule:

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

= - \frac{4 3}{8}

Cancel the common factor:

4

= - \frac{3}{2}

cos (- 4 θ + 150) = - \frac{3}{2}

cos (- 4 θ + 150) = - \frac{3}{2}

cos (- 4 θ + 150) = - \frac{3}{2}

General solutions for

cos (- 4 θ + 150) = - \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}

- 4 θ + 150 = \frac{5 π}{6} + 2 πn, - 4 θ + 150 = \frac{7 π}{6} + 2 πn

- 4 θ + 150 = \frac{5 π}{6} + 2 πn, - 4 θ + 150 = \frac{7 π}{6} + 2 πn

Solve

- 4 θ + 150 = \frac{5 π}{6} + 2 πn : θ = \frac{75}{2} - \frac{5 π}{24} - \frac{πn}{2}

- 4 θ + 150 = \frac{5 π}{6} + 2 πn

Move

150

to the right side

- 4 θ + 150 = \frac{5 π}{6} + 2 πn

Subtract

150

from both sides

- 4 θ + 150 - 150 = \frac{5 π}{6} + 2 πn - 150

Simplify

- 4 θ = \frac{5 π}{6} + 2 πn - 150

- 4 θ = \frac{5 π}{6} + 2 πn - 150

Divide both sides by

- 4

- 4 θ = \frac{5 π}{6} + 2 πn - 150

Divide both sides by

- 4

\frac{- 4 θ}{- 4} = \frac{\frac{5 π}{6}}{- 4} + \frac{2 πn}{- 4} - \frac{150}{- 4}

Simplify

\frac{- 4 θ}{- 4} = \frac{\frac{5 π}{6}}{- 4} + \frac{2 πn}{- 4} - \frac{150}{- 4}

Simplify

\frac{- 4 θ}{- 4} : θ

\frac{- 4 θ}{- 4}

Apply the fraction rule:

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

= \frac{4 θ}{4}

Divide the numbers:

\frac{4}{4} = 1

= θ

Simplify

\frac{\frac{5 π}{6}}{- 4} + \frac{2 πn}{- 4} - \frac{150}{- 4} : \frac{75}{2} - \frac{5 π}{24} - \frac{πn}{2}

\frac{\frac{5 π}{6}}{- 4} + \frac{2 πn}{- 4} - \frac{150}{- 4}

Group like terms

= - \frac{150}{- 4} + \frac{2 πn}{- 4} + \frac{\frac{5 π}{6}}{- 4}

\frac{150}{- 4} = - \frac{75}{2}

\frac{150}{- 4}

Apply the fraction rule:

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

= - \frac{150}{4}

Cancel the common factor:

2

= - \frac{75}{2}

\frac{2 πn}{- 4} = - \frac{πn}{2}

\frac{2 πn}{- 4}

Apply the fraction rule:

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

= - \frac{2 πn}{4}

Cancel the common factor:

2

= - \frac{πn}{2}

= - (- \frac{75}{2}) - \frac{πn}{2} + \frac{\frac{5 π}{6}}{- 4}

Apply rule

- (- a) = a

= \frac{75}{2} - \frac{πn}{2} + \frac{\frac{5 π}{6}}{- 4}

\frac{\frac{5 π}{6}}{- 4} = - \frac{5 π}{24}

\frac{\frac{5 π}{6}}{- 4}

Apply the fraction rule:

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

= - \frac{\frac{5 π}{6}}{4}

Apply the fraction rule:

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

\frac{\frac{5 π}{6}}{4} = \frac{5 π}{6 \cdot 4}

= - \frac{5 π}{6 \cdot 4}

Multiply the numbers:

6 \cdot 4 = 24

= - \frac{5 π}{24}

= \frac{75}{2} - \frac{πn}{2} - \frac{5 π}{24}

Group like terms

= \frac{75}{2} - \frac{5 π}{24} - \frac{πn}{2}

θ = \frac{75}{2} - \frac{5 π}{24} - \frac{πn}{2}

θ = \frac{75}{2} - \frac{5 π}{24} - \frac{πn}{2}

θ = \frac{75}{2} - \frac{5 π}{24} - \frac{πn}{2}

Solve

- 4 θ + 150 = \frac{7 π}{6} + 2 πn : θ = \frac{75}{2} - \frac{7 π}{24} - \frac{πn}{2}

- 4 θ + 150 = \frac{7 π}{6} + 2 πn

Move

150

to the right side

- 4 θ + 150 = \frac{7 π}{6} + 2 πn

Subtract

150

from both sides

- 4 θ + 150 - 150 = \frac{7 π}{6} + 2 πn - 150

Simplify

- 4 θ = \frac{7 π}{6} + 2 πn - 150

- 4 θ = \frac{7 π}{6} + 2 πn - 150

Divide both sides by

- 4

- 4 θ = \frac{7 π}{6} + 2 πn - 150

Divide both sides by

- 4

\frac{- 4 θ}{- 4} = \frac{\frac{7 π}{6}}{- 4} + \frac{2 πn}{- 4} - \frac{150}{- 4}

Simplify

\frac{- 4 θ}{- 4} = \frac{\frac{7 π}{6}}{- 4} + \frac{2 πn}{- 4} - \frac{150}{- 4}

Simplify

\frac{- 4 θ}{- 4} : θ

\frac{- 4 θ}{- 4}

Apply the fraction rule:

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

= \frac{4 θ}{4}

Divide the numbers:

\frac{4}{4} = 1

= θ

Simplify

\frac{\frac{7 π}{6}}{- 4} + \frac{2 πn}{- 4} - \frac{150}{- 4} : \frac{75}{2} - \frac{7 π}{24} - \frac{πn}{2}

\frac{\frac{7 π}{6}}{- 4} + \frac{2 πn}{- 4} - \frac{150}{- 4}

Group like terms

= - \frac{150}{- 4} + \frac{2 πn}{- 4} + \frac{\frac{7 π}{6}}{- 4}

\frac{150}{- 4} = - \frac{75}{2}

\frac{150}{- 4}

Apply the fraction rule:

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

= - \frac{150}{4}

Cancel the common factor:

2

= - \frac{75}{2}

\frac{2 πn}{- 4} = - \frac{πn}{2}

\frac{2 πn}{- 4}

Apply the fraction rule:

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

= - \frac{2 πn}{4}

Cancel the common factor:

2

= - \frac{πn}{2}

= - (- \frac{75}{2}) - \frac{πn}{2} + \frac{\frac{7 π}{6}}{- 4}

Apply rule

- (- a) = a

= \frac{75}{2} - \frac{πn}{2} + \frac{\frac{7 π}{6}}{- 4}

\frac{\frac{7 π}{6}}{- 4} = - \frac{7 π}{24}

\frac{\frac{7 π}{6}}{- 4}

Apply the fraction rule:

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

= - \frac{\frac{7 π}{6}}{4}

Apply the fraction rule:

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

\frac{\frac{7 π}{6}}{4} = \frac{7 π}{6 \cdot 4}

= - \frac{7 π}{6 \cdot 4}

Multiply the numbers:

6 \cdot 4 = 24

= - \frac{7 π}{24}

= \frac{75}{2} - \frac{πn}{2} - \frac{7 π}{24}

Group like terms

= \frac{75}{2} - \frac{7 π}{24} - \frac{πn}{2}

θ = \frac{75}{2} - \frac{7 π}{24} - \frac{πn}{2}

θ = \frac{75}{2} - \frac{7 π}{24} - \frac{πn}{2}

θ = \frac{75}{2} - \frac{7 π}{24} - \frac{πn}{2}

θ = \frac{75}{2} - \frac{5 π}{24} - \frac{πn}{2}, θ = \frac{75}{2} - \frac{7 π}{24} - \frac{πn}{2}

Graph

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