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

The general solution for 5cos(θ)+3=3cos(θ)+5 is θ=2pin

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Popular >

5cos(θ)+3=3cos(θ)+5

Solution

5 cos (θ) + 3 = 3 cos (θ) + 5

Solution

θ = 2 πn

Degrees

θ = 0^{\circ} + 36 0^{\circ} n

Solution steps

5 cos (θ) + 3 = 3 cos (θ) + 5

Solve by substitution

5 cos (θ) + 3 = 3 cos (θ) + 5

Let:

cos (θ) = u

5 u + 3 = 3 u + 5

5 u + 3 = 3 u + 5 : u = 1

5 u + 3 = 3 u + 5

Move

3

to the right side

5 u + 3 = 3 u + 5

Subtract

3

from both sides

5 u + 3 - 3 = 3 u + 5 - 3

Simplify

5 u = 3 u + 2

5 u = 3 u + 2

Move

3 u

to the left side

5 u = 3 u + 2

Subtract

3 u

from both sides

5 u - 3 u = 3 u + 2 - 3 u

Simplify

2 u = 2

2 u = 2

Divide both sides by

2

2 u = 2

Divide both sides by

2

\frac{2 u}{2} = \frac{2}{2}

Simplify

u = 1

u = 1

Substitute back

u = cos (θ)

cos (θ) = 1

cos (θ) = 1

cos (θ) = 1 : θ = 2 πn

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 = 0 + 2 πn

θ = 0 + 2 πn

Solve

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn

Combine all the solutions

θ = 2 πn

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Frequently Asked Questions (FAQ)

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