What is the general solution for 2+7cos(θ)=4sin^2(θ),-180<= x<= 180 ?

The general solution for 2+7cos(θ)=4sin^2(θ),-180<= x<= 180 is θ=1.31811…,θ=-1.31811…

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2+7cos(θ)=4sin^2(θ),-180<= x<= 180

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

θ = 1.31811 \dots, θ = - 1.31811 \dots

Solution steps

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

Subtract

4 sin^{2} (θ)

from both sides

2 + 7 cos (θ) - 4 sin^{2} (θ) = 0

Rewrite using trig identities

- 2 + 4 cos^{2} (θ) + 7 cos (θ) = 0

Solve by substitution

cos (θ) = \frac{1}{4}, cos (θ) = - 2

cos (θ) = \frac{1}{4}, - 18 0^{\circ} \leq x \leq 18 0^{\circ} : θ = arccos (\frac{1}{4}), θ = - arccos (\frac{1}{4})

cos (θ) = - 2, - 18 0^{\circ} \leq x \leq 18 0^{\circ} :

No Solution

Combine all the solutions

θ = arccos (\frac{1}{4}), θ = - arccos (\frac{1}{4})

Show solutions in decimal form

θ = 1.31811 \dots, θ = - 1.31811 \dots

1 = 2 cos (3 θ)

cos (4 θ) + cos (2 θ) = cos (θ)

(tan (x) + 3) (tan (x) + 2) = 0

2 tan (θ) + 6 = 0

8 = 8 cos (3 θ)

What is the general solution for 2+7cos(θ)=4sin^2(θ),-180<= x<= 180 ?
The general solution for 2+7cos(θ)=4sin^2(θ),-180<= x<= 180 is θ=1.31811…,θ=-1.31811…