What is the general solution for -2cos(θ-1)=0.5 ?

The general solution for -2cos(θ-1)=0.5 is θ=1.82347…+2pin+1,θ=-1.82347…+2pin+1

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Popular >

-2cos(θ-1)=0.5

Solution

- 2 cos (θ - 1) = 0.5

Solution

θ = 1.82347 \dots + 2 πn + 1, θ = - 1.82347 \dots + 2 πn + 1

Degrees

θ = 161.77329 \dots^{\circ} + 36 0^{\circ} n, θ = - 47.18173 \dots^{\circ} + 36 0^{\circ} n

Solution steps

- 2 cos (θ - 1) = 0.5

Divide both sides by

- 2

- 2 cos (θ - 1) = 0.5

Divide both sides by

- 2

\frac{- 2 cos ( θ - 1 )}{- 2} = \frac{0.5}{- 2}

Simplify

\frac{- 2 cos ( θ - 1 )}{- 2} = \frac{0.5}{- 2}

Simplify

\frac{- 2 cos ( θ - 1 )}{- 2} : cos (θ - 1)

\frac{- 2 cos ( θ - 1 )}{- 2}

Apply the fraction rule:

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

= \frac{2 cos ( θ - 1 )}{2}

Divide the numbers:

\frac{2}{2} = 1

= cos (θ - 1)

Simplify

\frac{0.5}{- 2} : - 0.25

\frac{0.5}{- 2}

Apply the fraction rule:

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

= - \frac{0.5}{2}

Divide the numbers:

\frac{0.5}{2} = 0.25

= - 0.25

cos (θ - 1) = - 0.25

cos (θ - 1) = - 0.25

cos (θ - 1) = - 0.25

Apply trig inverse properties

cos (θ - 1) = - 0.25

General solutions for

cos (θ - 1) = - 0.25

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

θ - 1 = arccos (- 0.25) + 2 πn, θ - 1 = - arccos (- 0.25) + 2 πn

θ - 1 = arccos (- 0.25) + 2 πn, θ - 1 = - arccos (- 0.25) + 2 πn

Solve

θ - 1 = arccos (- 0.25) + 2 πn : θ = arccos (- 0.25) + 2 πn + 1

θ - 1 = arccos (- 0.25) + 2 πn

Move

1

to the right side

θ - 1 = arccos (- 0.25) + 2 πn

Add

1

to both sides

θ - 1 + 1 = arccos (- 0.25) + 2 πn + 1

Simplify

θ = arccos (- 0.25) + 2 πn + 1

θ = arccos (- 0.25) + 2 πn + 1

Solve

θ - 1 = - arccos (- 0.25) + 2 πn : θ = - arccos (- 0.25) + 2 πn + 1

θ - 1 = - arccos (- 0.25) + 2 πn

Move

1

to the right side

θ - 1 = - arccos (- 0.25) + 2 πn

Add

1

to both sides

θ - 1 + 1 = - arccos (- 0.25) + 2 πn + 1

Simplify

θ = - arccos (- 0.25) + 2 πn + 1

θ = - arccos (- 0.25) + 2 πn + 1

θ = arccos (- 0.25) + 2 πn + 1, θ = - arccos (- 0.25) + 2 πn + 1

Show solutions in decimal form

θ = 1.82347 \dots + 2 πn + 1, θ = - 1.82347 \dots + 2 πn + 1

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Frequently Asked Questions (FAQ)

What is the general solution for -2cos(θ-1)=0.5 ?
The general solution for -2cos(θ-1)=0.5 is θ=1.82347…+2pin+1,θ=-1.82347…+2pin+1