What is the general solution for -9sin^2(x)-5cos(x)+5=0 ?

The general solution for -9sin^2(x)-5cos(x)+5=0 is x=2pin,x=2.03135…+2pin,x=-2.03135…+2pin

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-9sin^2(x)-5cos(x)+5=0

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

x = 2 πn, x = 2.03135 \dots + 2 πn, x = - 2.03135 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

- 4 - 5 cos (x) + 9 cos^{2} (x) = 0

Solve by substitution

cos (x) = 1, cos (x) = - \frac{4}{9}

cos (x) = 1 : x = 2 πn

cos (x) = - \frac{4}{9} : x = arccos (- \frac{4}{9}) + 2 πn, x = - arccos (- \frac{4}{9}) + 2 πn

Combine all the solutions

x = 2 πn, x = arccos (- \frac{4}{9}) + 2 πn, x = - arccos (- \frac{4}{9}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = 2.03135 \dots + 2 πn, x = - 2.03135 \dots + 2 πn

cos (t) = - \frac{3}{5}

2 - sin (θ) = 3 sin (θ)

- cos (\frac{x}{2}) + sin (\frac{x}{2}) = \frac{2}{5}

\frac{35}{sin ( 9 0 ^{\circ} )} = \frac{27}{sin ( y )}

4 cos^{2} (x) + 2 cos (x) - 22 cos (x) = 2

What is the general solution for -9sin^2(x)-5cos(x)+5=0 ?
The general solution for -9sin^2(x)-5cos(x)+5=0 is x=2pin,x=2.03135…+2pin,x=-2.03135…+2pin