What is the general solution for -4cos(2θ)-19=-26cos(θ),0<= θ<360 ?

The general solution for -4cos(2θ)-19=-26cos(θ),0<= θ<360 is θ=0.72273…,θ=360-0.72273…

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-4cos(2θ)-19=-26cos(θ),0<= θ<360

- 4 cos (2 θ) - 19 = - 26 cos (θ), 0 \leq θ < 36 0^{\circ}

θ = 0.72273 \dots, θ = 36 0^{\circ} - 0.72273 \dots

Solution steps

- 4 cos (2 θ) - 19 = - 26 cos (θ), 0 \leq θ < 36 0^{\circ}

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}, 0 \leq θ < 36 0^{\circ} : θ = arccos (\frac{3}{4}), θ = 36 0^{\circ} - arccos (\frac{3}{4})

cos (θ) = \frac{5}{2}, 0 \leq θ < 36 0^{\circ} :

No Solution

Combine all the solutions

θ = arccos (\frac{3}{4}), θ = 36 0^{\circ} - arccos (\frac{3}{4})

Show solutions in decimal form

θ = 0.72273 \dots, θ = 36 0^{\circ} - 0.72273 \dots

3 cos^{2} (x) = 7 - 8 sin (x)

sin (X) = - \frac{1}{2}

- 2 (sin (2 t) - cos (t)) = 0

5 cos (A) + 8 = 3 cos (A) + 6

2 + 7 cos (θ) = 4 sin^{2} (θ), - 18 0^{\circ} \leq x \leq 18 0^{\circ}

What is the general solution for -4cos(2θ)-19=-26cos(θ),0<= θ<360 ?
The general solution for -4cos(2θ)-19=-26cos(θ),0<= θ<360 is θ=0.72273…,θ=360-0.72273…