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

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

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5cos^2(x)=6sin(x)

5 cos^{2} (x) = 6 sin (x)

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

Solution steps

5 cos^{2} (x) = 6 sin (x)

Subtract

6 sin (x)

from both sides

5 cos^{2} (x) - 6 sin (x) = 0

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = - \frac{3 + 34}{5} :

No Solution

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

Combine all the solutions

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

Show solutions in decimal form

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

sec^{2} (x) = 2 tan (x) + 4

- 4 cos (θ) = - sin^{2} (θ) + 1

2 sin^{2} (θ) + 3 sin (θ) = 0, 0 \leq θ < 2 π

sin (θ) = \frac{π}{2}

arcsin (\frac{900 x ^{2} - 1}{900 x ^{2} + 1}) = 1.18

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