What is the general solution for 7cos^2(θ)+5=2sin(θ)+7 ?

The general solution for 7cos^2(θ)+5=2sin(θ)+7 is θ=(3pi)/2+2pin,θ=0.79560…+2pin,θ=pi-0.79560…+2pin

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7cos^2(θ)+5=2sin(θ)+7

7 cos^{2} (θ) + 5 = 2 sin (θ) + 7

θ = \frac{3 π}{2} + 2 πn, θ = 0.79560 \dots + 2 πn, θ = π - 0.79560 \dots + 2 πn

Solution steps

7 cos^{2} (θ) + 5 = 2 sin (θ) + 7

Subtract

2 sin (θ) + 7

from both sides

7 cos^{2} (θ) - 2 sin (θ) - 2 = 0

Rewrite using trig identities

5 - 2 sin (θ) - 7 sin^{2} (θ) = 0

Solve by substitution

sin (θ) = - 1, sin (θ) = \frac{5}{7}

sin (θ) = - 1 : θ = \frac{3 π}{2} + 2 πn

sin (θ) = \frac{5}{7} : θ = arcsin (\frac{5}{7}) + 2 πn, θ = π - arcsin (\frac{5}{7}) + 2 πn

Combine all the solutions

θ = \frac{3 π}{2} + 2 πn, θ = arcsin (\frac{5}{7}) + 2 πn, θ = π - arcsin (\frac{5}{7}) + 2 πn

Show solutions in decimal form

θ = \frac{3 π}{2} + 2 πn, θ = 0.79560 \dots + 2 πn, θ = π - 0.79560 \dots + 2 πn

1 - cos (2 x) = 1 + cos (2 x)

5 cos^{2} (x) - 10 cos (x) + 5 = 0

3 sin (x) - 2 sin (x) cos (x) = 0

8 tan (b) + 12 = 3 tan (b) + 7

sin (θ) + 2 = - sin (θ)

What is the general solution for 7cos^2(θ)+5=2sin(θ)+7 ?
The general solution for 7cos^2(θ)+5=2sin(θ)+7 is θ=(3pi)/2+2pin,θ=0.79560…+2pin,θ=pi-0.79560…+2pin