What is the general solution for 3+4cos(θ)=-1 ?

The general solution for 3+4cos(θ)=-1 is θ=pi+2pin

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3+4cos(θ)=-1

3 + 4 cos (θ) = - 1

θ = π + 2 πn

Degrees

θ = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

3 + 4 cos (θ) = - 1

Move

3

to the right side

3 + 4 cos (θ) = - 1

Subtract

3

from both sides

3 + 4 cos (θ) - 3 = - 1 - 3

Simplify

4 cos (θ) = - 4

4 cos (θ) = - 4

Divide both sides by

4

4 cos (θ) = - 4

Divide both sides by

4

\frac{4 cos ( θ )}{4} = \frac{- 4}{4}

Simplify

cos (θ) = - 1

cos (θ) = - 1

General solutions for

cos (θ) = - 1

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 = π + 2 πn

θ = π + 2 πn

cot (x) tan (x) = sec (x) csc (x)

sin (x + \frac{π}{2}) - sin (x - \frac{π}{2}) = 2

x, tan (x) csc (x) = \frac{1}{f}

sin (x) = \frac{10.7}{71.5}

cos (y) = 1

What is the general solution for 3+4cos(θ)=-1 ?
The general solution for 3+4cos(θ)=-1 is θ=pi+2pin