What is the general solution for sin(x)=-1/(sqrt(10)) ?

The general solution for sin(x)=-1/(sqrt(10)) is x=-0.32175…+2pin,x=pi+0.32175…+2pin

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sin(x)=-1/(sqrt(10))

sin (x) = - \frac{1}{10}

x = - 0.32175 \dots + 2 πn, x = π + 0.32175 \dots + 2 πn

Solution steps

sin (x) = - \frac{1}{10}

Simplify

- \frac{1}{10} : - \frac{10}{10}

Apply trig inverse properties

x = arcsin (- \frac{10}{10}) + 2 πn, x = π + arcsin (\frac{10}{10}) + 2 πn

Show solutions in decimal form

x = - 0.32175 \dots + 2 πn, x = π + 0.32175 \dots + 2 πn

sec^{2} (θ) + sec (θ) = 2, 2 π \leq θ \leq 3 π

6 sec^{2} (x) = 0

3 - 2 cos (x) = 2

tan (θ) = - \frac{8}{5}

sin (θ) - 0.1 \cdot cos (θ) = 0.56632

What is the general solution for sin(x)=-1/(sqrt(10)) ?
The general solution for sin(x)=-1/(sqrt(10)) is x=-0.32175…+2pin,x=pi+0.32175…+2pin