What is the general solution for 3cos^2(x)+4sin(x)-4=0 ?

The general solution for 3cos^2(x)+4sin(x)-4=0 is x=0.33983…+2pin,x=pi-0.33983…+2pin,x= pi/2+2pin

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3cos^2(x)+4sin(x)-4=0

3 cos^{2} (x) + 4 sin (x) - 4 = 0

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

3 cos^{2} (x) + 4 sin (x) - 4 = 0

Rewrite using trig identities

- 1 - 3 sin^{2} (x) + 4 sin (x) = 0

Solve by substitution

sin (x) = \frac{1}{3}, sin (x) = 1

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn, x = \frac{π}{2} + 2 πn

Show solutions in decimal form

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn, x = \frac{π}{2} + 2 πn

sin (x) = \frac{7}{15}

3 sec (x) = 9

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

x, sin (2 x) = \frac{1}{2}

- 4 sin (x) = - cos^{2} (x) + 4, 0 \leq x \leq 2 π

What is the general solution for 3cos^2(x)+4sin(x)-4=0 ?
The general solution for 3cos^2(x)+4sin(x)-4=0 is x=0.33983…+2pin,x=pi-0.33983…+2pin,x= pi/2+2pin