What is the general solution for cos^2(x)-3sin(x)=0 ?

The general solution for cos^2(x)-3sin(x)=0 is x=0.30760…+2pin,x=pi-0.30760…+2pin

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

cos^{2} (x) - 3 sin (x) = 0

x = 0.30760 \dots + 2 πn, x = π - 0.30760 \dots + 2 πn

Solution steps

cos^{2} (x) - 3 sin (x) = 0

Rewrite using trig identities

1 - sin^{2} (x) - 3 sin (x) = 0

Solve by substitution

sin (x) = - \frac{3 + 13}{2}, sin (x) = \frac{13 - 3}{2}

sin (x) = - \frac{3 + 13}{2} :

No Solution

sin (x) = \frac{13 - 3}{2} : x = arcsin (\frac{13 - 3}{2}) + 2 πn, x = π - arcsin (\frac{13 - 3}{2}) + 2 πn

Combine all the solutions

x = arcsin (\frac{13 - 3}{2}) + 2 πn, x = π - arcsin (\frac{13 - 3}{2}) + 2 πn

Show solutions in decimal form

x = 0.30760 \dots + 2 πn, x = π - 0.30760 \dots + 2 πn

csc (t) = \frac{1}{- \frac{2}{2}}

cos^{2} (x) = 1 - sin (x), 0 \leq x < 2 π

cos (2 x) - 3 sin (x) = 2, 0^{\circ} \leq x \leq 36 0^{\circ}

2 cos^{2} (x) + 3 cos (x) = 4 cos (x) + 1

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

What is the general solution for cos^2(x)-3sin(x)=0 ?
The general solution for cos^2(x)-3sin(x)=0 is x=0.30760…+2pin,x=pi-0.30760…+2pin