What is the general solution for sin^2(x)+6sin(x)=5 ?

The general solution for sin^2(x)+6sin(x)=5 is x=0.83553…+2pin,x=pi-0.83553…+2pin

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sin^2(x)+6sin(x)=5

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

x = 0.83553 \dots + 2 πn, x = π - 0.83553 \dots + 2 πn

Solution steps

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

Solve by substitution

sin (x) = - 3 + 14, sin (x) = - 3 - 14

sin (x) = - 3 + 14 : x = arcsin (- 3 + 14) + 2 πn, x = π - arcsin (- 3 + 14) + 2 πn

sin (x) = - 3 - 14 :

No Solution

Combine all the solutions

x = arcsin (- 3 + 14) + 2 πn, x = π - arcsin (- 3 + 14) + 2 πn

Show solutions in decimal form

x = 0.83553 \dots + 2 πn, x = π - 0.83553 \dots + 2 πn

x, y + y = tan (x)

cos (2 x) = \frac{1}{13}

cos (θ) = 0, D = R (θ)

\frac{sin ( θ )}{20} = \frac{sin ( 15 0 ^{\circ} )}{58.1826}

tan (x) = \frac{6}{3}

What is the general solution for sin^2(x)+6sin(x)=5 ?
The general solution for sin^2(x)+6sin(x)=5 is x=0.83553…+2pin,x=pi-0.83553…+2pin