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

The general solution for 5cos^2(a)-2sin(a)-2=0 is a=(3pi)/2+2pin,a=0.64350…+2pin,a=pi-0.64350…+2pin

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5cos^2(a)-2sin(a)-2=0

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

a = \frac{3 π}{2} + 2 πn, a = 0.64350 \dots + 2 πn, a = π - 0.64350 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

3 - 2 sin (a) - 5 sin^{2} (a) = 0

Solve by substitution

sin (a) = - 1, sin (a) = \frac{3}{5}

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

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

Combine all the solutions

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

Show solutions in decimal form

a = \frac{3 π}{2} + 2 πn, a = 0.64350 \dots + 2 πn, a = π - 0.64350 \dots + 2 πn

tan^{2} (a) = \frac{( 2 tan ( a ) )}{( 1 - tan ^{2} ( a ) )}

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

cos^{2} (a) = \frac{2}{3}

sin (2 x) = - 0.848055484

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

What is the general solution for 5cos^2(a)-2sin(a)-2=0 ?
The general solution for 5cos^2(a)-2sin(a)-2=0 is a=(3pi)/2+2pin,a=0.64350…+2pin,a=pi-0.64350…+2pin