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

Solution

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

x = - 0.38246 \dots + 2 πn, x = π + 0.38246 \dots + 2 πn, x = 0.63780 \dots + 2 πn, x = π - 0.63780 \dots + 2 πn

Solution steps

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

Solve by substitution

sin (x) = - \frac{- 1 + 19}{9}, sin (x) = \frac{1 + 19}{9}

sin (x) = - \frac{- 1 + 19}{9} : x = arcsin (- \frac{- 1 + 19}{9}) + 2 πn, x = π + arcsin (\frac{- 1 + 19}{9}) + 2 πn

sin (x) = \frac{1 + 19}{9} : x = arcsin (\frac{1 + 19}{9}) + 2 πn, x = π - arcsin (\frac{1 + 19}{9}) + 2 πn

Combine all the solutions

x = arcsin (- \frac{- 1 + 19}{9}) + 2 πn, x = π + arcsin (\frac{- 1 + 19}{9}) + 2 πn, x = arcsin (\frac{1 + 19}{9}) + 2 πn, x = π - arcsin (\frac{1 + 19}{9}) + 2 πn

Show solutions in decimal form

x = - 0.38246 \dots + 2 πn, x = π + 0.38246 \dots + 2 πn, x = 0.63780 \dots + 2 πn, x = π - 0.63780 \dots + 2 πn

cos^{2} (x) - 2 cos (x) + 1 = 0, 0^{\circ} 36 0^{\circ}

sin^{4} (x) = sin^{2} (x), 0 \leq x < 2 π

sin (θ) - 0.1 cos (θ) = \frac{6.88}{9.8}

sin (x) = 0.3352

tan^{2} (3 y) - 2 sec (3 y) - 2 = 0