What is the general solution for sin^2(x)+8sin(x)-1=0 ?

The general solution for sin^2(x)+8sin(x)-1=0 is x=0.12341…+2pin,x=pi-0.12341…+2pin

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sin^2(x)+8sin(x)-1=0

sin^{2} (x) + 8 sin (x) - 1 = 0

x = 0.12341 \dots + 2 πn, x = π - 0.12341 \dots + 2 πn

Solution steps

sin^{2} (x) + 8 sin (x) - 1 = 0

Solve by substitution

sin (x) = - 4 + 17, sin (x) = - 4 - 17

sin (x) = - 4 + 17 : x = arcsin (- 4 + 17) + 2 πn, x = π - arcsin (- 4 + 17) + 2 πn

sin (x) = - 4 - 17 :

No Solution

Combine all the solutions

x = arcsin (- 4 + 17) + 2 πn, x = π - arcsin (- 4 + 17) + 2 πn

Show solutions in decimal form

x = 0.12341 \dots + 2 πn, x = π - 0.12341 \dots + 2 πn

x, y = arctan (2 x + 3 y)

sin (2 x) = 0.89583

tan (θ) = 1.234, θ

x, sin (x) cos (x) = sin (x + p) cos (x + p)

sin (θ) = \frac{3}{5}, cos (2 θ)

What is the general solution for sin^2(x)+8sin(x)-1=0 ?
The general solution for sin^2(x)+8sin(x)-1=0 is x=0.12341…+2pin,x=pi-0.12341…+2pin