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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3cos(θ-55)=-1.56

3 cos (θ - 5 5^{\circ}) = - 1.56

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

Solution steps

3 cos (θ - 5 5^{\circ}) = - 1.56

Divide both sides by

3

cos (θ - 5 5^{\circ}) = - 0.52

Apply trig inverse properties

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}

Solve

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

cot (3 x) = 3

sin (2 θ) - sin (θ) = 0

- 4 sin (4 x) = 0

cos (x) = - 3

2 cos (3 θ) = 1

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