What is the general solution for 4(sin(x))^2-15sin(x)-4=0 ?

The general solution for 4(sin(x))^2-15sin(x)-4=0 is x=-0.25268…+2pin,x=pi+0.25268…+2pin

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4(sin(x))^2-15sin(x)-4=0

4 (sin (x))^{2} - 15 sin (x) - 4 = 0

x = - 0.25268 \dots + 2 πn, x = π + 0.25268 \dots + 2 πn

Solution steps

4 (sin (x))^{2} - 15 sin (x) - 4 = 0

Solve by substitution

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

sin (x) = 4 :

No Solution

sin (x) = - \frac{1}{4} : x = arcsin (- \frac{1}{4}) + 2 πn, x = π + arcsin (\frac{1}{4}) + 2 πn

Combine all the solutions

x = arcsin (- \frac{1}{4}) + 2 πn, x = π + arcsin (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = - 0.25268 \dots + 2 πn, x = π + 0.25268 \dots + 2 πn

1 + sin (θ) = 1 + sin (- θ)

cos (2 x) = 2 + 3 sin (x), \frac{π}{2} \leq x \leq \frac{3 π}{2}

tan (θ) = (\frac{3}{8})

29 = \frac{1}{2} (5.6) (7.1) sin (x)

\frac{10.4}{sin ( x )} = \frac{12}{sin ( 6 2 ^{\circ} )}

What is the general solution for 4(sin(x))^2-15sin(x)-4=0 ?
The general solution for 4(sin(x))^2-15sin(x)-4=0 is x=-0.25268…+2pin,x=pi+0.25268…+2pin