What is the general solution for -4cos(2θ)-19=-26cos(θ) ?

The general solution for -4cos(2θ)-19=-26cos(θ) is θ=0.72273…+2pin,θ=2pi-0.72273…+2pin

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-4cos(2θ)-19=-26cos(θ)

- 4 cos (2 θ) - 19 = - 26 cos (θ)

θ = 0.72273 \dots + 2 πn, θ = 2 π - 0.72273 \dots + 2 πn

Solution steps

- 4 cos (2 θ) - 19 = - 26 cos (θ)

Subtract

- 26 cos (θ)

from both sides

- 4 cos (2 θ) - 19 + 26 cos (θ) = 0

Rewrite using trig identities

- 15 + 26 cos (θ) - 8 cos^{2} (θ) = 0

Solve by substitution

cos (θ) = \frac{3}{4}, cos (θ) = \frac{5}{2}

cos (θ) = \frac{3}{4} : θ = arccos (\frac{3}{4}) + 2 πn, θ = 2 π - arccos (\frac{3}{4}) + 2 πn

cos (θ) = \frac{5}{2} :

No Solution

Combine all the solutions

θ = arccos (\frac{3}{4}) + 2 πn, θ = 2 π - arccos (\frac{3}{4}) + 2 πn

Show solutions in decimal form

θ = 0.72273 \dots + 2 πn, θ = 2 π - 0.72273 \dots + 2 πn

x, z = e^{y} - 3 sin (x y)

tan (4 x + 6) = - 0.272

7 sin (θ) + 22 = 0

\frac{1}{2} sinh (2 x) - \frac{4}{5} cosh (2 x) + 1 = 0

7 sin^{2} (x) + 2 sin (x) - 2 = 0

What is the general solution for -4cos(2θ)-19=-26cos(θ) ?
The general solution for -4cos(2θ)-19=-26cos(θ) is θ=0.72273…+2pin,θ=2pi-0.72273…+2pin