What is the general solution for 9sin(x-0.5pi)+8=0 ?

The general solution for 9sin(x-0.5pi)+8=0 is x=-1.09491…+2pin+0.5pi,x=1.5pi+2pin+1.09491…

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9sin(x-0.5pi)+8=0

9 sin (x - 0.5 π) + 8 = 0

x = - 1.09491 \dots + 2 πn + 0.5 π, x = 1.5 π + 2 πn + 1.09491 \dots

Solution steps

9 sin (x - 0.5 π) + 8 = 0

Move

8

to the right side

9 sin (x - 0.5 π) = - 8

Divide both sides by

9

sin (x - 0.5 π) = - \frac{8}{9}

Apply trig inverse properties

x - 0.5 π = arcsin (- \frac{8}{9}) + 2 πn, x - 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn

Solve

x - 0.5 π = arcsin (- \frac{8}{9}) + 2 πn : x = - arcsin (\frac{8}{9}) + 2 πn + 0.5 π

Solve

x - 0.5 π = π + arcsin (\frac{8}{9}) + 2 πn : x = 1.5 π + 2 πn + arcsin (\frac{8}{9})

x = - arcsin (\frac{8}{9}) + 2 πn + 0.5 π, x = 1.5 π + 2 πn + arcsin (\frac{8}{9})

Show solutions in decimal form

x = - 1.09491 \dots + 2 πn + 0.5 π, x = 1.5 π + 2 πn + 1.09491 \dots

sec (- 13 5^{\circ}) - cot (x) = 2

csc (x - 3 0^{\circ}) = 2

- cos^{2} (x) + 4 cos (x) = 0

sin^{2} (x) + 5 cos^{2} (x) = 3

sin (x - \frac{π}{2}) + cos (x + \frac{π}{2}) = 0

What is the general solution for 9sin(x-0.5pi)+8=0 ?
The general solution for 9sin(x-0.5pi)+8=0 is x=-1.09491…+2pin+0.5pi,x=1.5pi+2pin+1.09491…