What is the general solution for 3cos(θ-55)=-1.56 ?

The general solution for 3cos(θ-55)=-1.56 is θ=2.11764…+360n+55,θ=-2.11764…+360n+55

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Popular Trigonometry >

3cos(θ-55)=-1.56

Solution

3 cos (θ - 5 5^{\circ}) = - 1.56

Solution

θ = 2.11764 \dots + 36 0^{\circ} n + 5 5^{\circ}, θ = - 2.11764 \dots + 36 0^{\circ} n + 5 5^{\circ}

Radians

θ = 2.11764 \dots + \frac{11 π}{36} + 2 πn, θ = - 2.11764 \dots + \frac{11 π}{36} + 2 πn

Solution steps

3 cos (θ - 5 5^{\circ}) = - 1.56

Divide both sides by

3

3 cos (θ - 5 5^{\circ}) = - 1.56

Divide both sides by

3

\frac{3 cos ( θ - 5 5 ^{\circ} )}{3} = \frac{- 1.56}{3}

Simplify

\frac{3 cos ( θ - 5 5 ^{\circ} )}{3} = \frac{- 1.56}{3}

Simplify

\frac{3 cos ( θ - 5 5 ^{\circ} )}{3} : cos (θ - 5 5^{\circ})

\frac{3 cos ( θ - 5 5 ^{\circ} )}{3}

Divide the numbers:

\frac{3}{3} = 1

= cos (θ - 5 5^{\circ})

Simplify

\frac{- 1.56}{3} : - 0.52

\frac{- 1.56}{3}

Apply the fraction rule:

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

= - \frac{1.56}{3}

Divide the numbers:

\frac{1.56}{3} = 0.52

= - 0.52

cos (θ - 5 5^{\circ}) = - 0.52

cos (θ - 5 5^{\circ}) = - 0.52

cos (θ - 5 5^{\circ}) = - 0.52

Apply trig inverse properties

cos (θ - 5 5^{\circ}) = - 0.52

General solutions for

cos (θ - 5 5^{\circ}) = - 0.52

cos (x) = - a \Rightarrow x = arccos (- a) + 36 0^{\circ} n, x = - arccos (- a) + 36 0^{\circ} n

θ - 5 5^{\circ} = arccos (- 0.52) + 36 0^{\circ} n, θ - 5 5^{\circ} = - arccos (- 0.52) + 36 0^{\circ} n

θ - 5 5^{\circ} = arccos (- 0.52) + 36 0^{\circ} n, θ - 5 5^{\circ} = - arccos (- 0.52) + 36 0^{\circ} n

Solve

θ - 5 5^{\circ} = arccos (- 0.52) + 36 0^{\circ} n : θ = arccos (- 0.52) + 36 0^{\circ} n + 5 5^{\circ}

θ - 5 5^{\circ} = arccos (- 0.52) + 36 0^{\circ} n

Move

5 5^{\circ}

to the right side

θ - 5 5^{\circ} = arccos (- 0.52) + 36 0^{\circ} n

Add

5 5^{\circ}

to both sides

θ - 5 5^{\circ} + 5 5^{\circ} = arccos (- 0.52) + 36 0^{\circ} n + 5 5^{\circ}

Simplify

θ = arccos (- 0.52) + 36 0^{\circ} n + 5 5^{\circ}

θ = arccos (- 0.52) + 36 0^{\circ} n + 5 5^{\circ}

Solve

θ - 5 5^{\circ} = - arccos (- 0.52) + 36 0^{\circ} n : θ = - arccos (- 0.52) + 36 0^{\circ} n + 5 5^{\circ}

θ - 5 5^{\circ} = - arccos (- 0.52) + 36 0^{\circ} n

Move

5 5^{\circ}

to the right side

θ - 5 5^{\circ} = - arccos (- 0.52) + 36 0^{\circ} n

Add

5 5^{\circ}

to both sides

θ - 5 5^{\circ} + 5 5^{\circ} = - arccos (- 0.52) + 36 0^{\circ} n + 5 5^{\circ}

Simplify

θ = - arccos (- 0.52) + 36 0^{\circ} n + 5 5^{\circ}

θ = - arccos (- 0.52) + 36 0^{\circ} n + 5 5^{\circ}

θ = arccos (- 0.52) + 36 0^{\circ} n + 5 5^{\circ}, θ = - arccos (- 0.52) + 36 0^{\circ} n + 5 5^{\circ}

Show solutions in decimal form

θ = 2.11764 \dots + 36 0^{\circ} n + 5 5^{\circ}, θ = - 2.11764 \dots + 36 0^{\circ} n + 5 5^{\circ}

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Frequently Asked Questions (FAQ)

What is the general solution for 3cos(θ-55)=-1.56 ?
The general solution for 3cos(θ-55)=-1.56 is θ=2.11764…+360n+55,θ=-2.11764…+360n+55