What is the general solution for 1+4sin(x)=0 ?

The general solution for 1+4sin(x)=0 is x=-0.25268…+2pin,x=pi+0.25268…+2pin

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1+4sin(x)=0

1 + 4 sin (x) = 0

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

Solution steps

1 + 4 sin (x) = 0

Move

1

to the right side

4 sin (x) = - 1

Divide both sides by

4

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

Apply trig inverse properties

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

cos^{2} (x) = \frac{3}{2} sin (x)

sin (x) = cos (\frac{x}{2})

cos (\frac{π ( x - 7 )}{3}) = \frac{1}{2}

2 cos (2 x) + 8 cos (x) + 5 = 0

sin (x) \cdot tan (x) = 3 \cdot sin (x)

What is the general solution for 1+4sin(x)=0 ?
The general solution for 1+4sin(x)=0 is x=-0.25268…+2pin,x=pi+0.25268…+2pin