What is the general solution for 5sin(x)=-3 ?

The general solution for 5sin(x)=-3 is x=-0.64350…+2pin,x=pi+0.64350…+2pin

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5sin(x)=-3

5 sin (x) = - 3

x = - 0.64350 \dots + 2 πn, x = π + 0.64350 \dots + 2 πn

Degrees

x = - 36.86989 \dots^{\circ} + 36 0^{\circ} n, x = 216.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

5 sin (x) = - 3

Divide both sides by

5

5 sin (x) = - 3

Divide both sides by

5

\frac{5 sin ( x )}{5} = \frac{- 3}{5}

Simplify

sin (x) = - \frac{3}{5}

sin (x) = - \frac{3}{5}

Apply trig inverse properties

sin (x) = - \frac{3}{5}

General solutions for

sin (x) = - \frac{3}{5}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{3}{5}) + 2 πn, x = π + arcsin (\frac{3}{5}) + 2 πn

x = arcsin (- \frac{3}{5}) + 2 πn, x = π + arcsin (\frac{3}{5}) + 2 πn

Show solutions in decimal form

x = - 0.64350 \dots + 2 πn, x = π + 0.64350 \dots + 2 πn

csc^{2} (x) = 2 \cdot cot^{2} (x)

3 sin (2 x) = cos (2 x)

3 \cdot 2 = \frac{50 sin ( x )}{9.8}

cos (2 x + 5) = sin (2 x)

sin (2 θ) + 3 cos (θ) = cos (θ)

What is the general solution for 5sin(x)=-3 ?
The general solution for 5sin(x)=-3 is x=-0.64350…+2pin,x=pi+0.64350…+2pin