What is the general solution for 5cos(θ)=-3 ?

The general solution for 5cos(θ)=-3 is θ=2.21429…+2pin,θ=-2.21429…+2pin

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5cos(θ)=-3

5 cos (θ) = - 3

θ = 2.21429 \dots + 2 πn, θ = - 2.21429 \dots + 2 πn

Degrees

θ = 126.86989 \dots^{\circ} + 36 0^{\circ} n, θ = - 126.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

5 cos (θ) = - 3

Divide both sides by

5

5 cos (θ) = - 3

Divide both sides by

5

\frac{5 cos ( θ )}{5} = \frac{- 3}{5}

Simplify

cos (θ) = - \frac{3}{5}

cos (θ) = - \frac{3}{5}

Apply trig inverse properties

cos (θ) = - \frac{3}{5}

General solutions for

cos (θ) = - \frac{3}{5}

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

θ = arccos (- \frac{3}{5}) + 2 πn, θ = - arccos (- \frac{3}{5}) + 2 πn

θ = arccos (- \frac{3}{5}) + 2 πn, θ = - arccos (- \frac{3}{5}) + 2 πn

Show solutions in decimal form

θ = 2.21429 \dots + 2 πn, θ = - 2.21429 \dots + 2 πn

sec^{2} (x) - sec (x) = 0

4 cos^{2} (x) - 2 cos (x) - 3 = 0

3 cos (x) = \frac{6}{π}

6 cos (2 θ) = 18 cos (θ) - 12

cos (\frac{2}{3} x - \frac{π}{2}) = 1

What is the general solution for 5cos(θ)=-3 ?
The general solution for 5cos(θ)=-3 is θ=2.21429…+2pin,θ=-2.21429…+2pin