What is the general solution for 5cos^2(θ)=6sin(θ) ?

The general solution for 5cos^2(θ)=6sin(θ) is θ=0.60187…+2pin,θ=pi-0.60187…+2pin

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5cos^2(θ)=6sin(θ)

5 cos^{2} (θ) = 6 sin (θ)

θ = 0.60187 \dots + 2 πn, θ = π - 0.60187 \dots + 2 πn

Solution steps

5 cos^{2} (θ) = 6 sin (θ)

Subtract

6 sin (θ)

from both sides

5 cos^{2} (θ) - 6 sin (θ) = 0

Rewrite using trig identities

(1 - sin^{2} (θ)) \cdot 5 - 6 sin (θ) = 0

Solve by substitution

sin (θ) = - \frac{3 + 34}{5}, sin (θ) = \frac{34 - 3}{5}

sin (θ) = - \frac{3 + 34}{5} :

No Solution

sin (θ) = \frac{34 - 3}{5} : θ = arcsin (\frac{34 - 3}{5}) + 2 πn, θ = π - arcsin (\frac{34 - 3}{5}) + 2 πn

Combine all the solutions

θ = arcsin (\frac{34 - 3}{5}) + 2 πn, θ = π - arcsin (\frac{34 - 3}{5}) + 2 πn

Show solutions in decimal form

θ = 0.60187 \dots + 2 πn, θ = π - 0.60187 \dots + 2 πn

8 tan (θ) = 0

12 cos^{2} (x) + 11 cos (x) - 5 = 0

2 cos^{2} (x) + 3 cos (x) + 1 = 0, 0 \leq x \leq 2 π

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

21 + 18 cos (x) = 16 sin^{2} (x)

What is the general solution for 5cos^2(θ)=6sin(θ) ?
The general solution for 5cos^2(θ)=6sin(θ) is θ=0.60187…+2pin,θ=pi-0.60187…+2pin