What is the general solution for 2sin^2(x)-5sin(x)-4=0 ?

The general solution for 2sin^2(x)-5sin(x)-4=0 is x=-0.69119…+2pin,x=pi+0.69119…+2pin

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2sin^2(x)-5sin(x)-4=0

2 sin^{2} (x) - 5 sin (x) - 4 = 0

x = - 0.69119 \dots + 2 πn, x = π + 0.69119 \dots + 2 πn

Solution steps

2 sin^{2} (x) - 5 sin (x) - 4 = 0

Solve by substitution

sin (x) = \frac{5 + 57}{4}, sin (x) = \frac{5 - 57}{4}

sin (x) = \frac{5 + 57}{4} :

No Solution

sin (x) = \frac{5 - 57}{4} : x = arcsin (\frac{5 - 57}{4}) + 2 πn, x = π + arcsin (- \frac{5 - 57}{4}) + 2 πn

Combine all the solutions

x = arcsin (\frac{5 - 57}{4}) + 2 πn, x = π + arcsin (- \frac{5 - 57}{4}) + 2 πn

Show solutions in decimal form

x = - 0.69119 \dots + 2 πn, x = π + 0.69119 \dots + 2 πn

sin (θ) = 0.4815

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

sin (A) = \frac{4}{5}, sin (2 A)

\frac{1}{2} (1 + cos (x)) = 0.6294095226

2 + 2 cos (x) = 6 cos (x)

What is the general solution for 2sin^2(x)-5sin(x)-4=0 ?
The general solution for 2sin^2(x)-5sin(x)-4=0 is x=-0.69119…+2pin,x=pi+0.69119…+2pin