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

Radians

x = - 0.32175 \dots + 6.28318 \dots n, x = π + 0.32175 \dots + 6.28318 \dots n

Solution steps

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

Simplify

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

- \frac{1}{10}

Multiply by the conjugate

\frac{10}{10}

= - \frac{1 \cdot 10}{10 10}

1 \cdot 10 = 10

1010 = 10

1010

Apply radical rule:

a a = a

1010 = 10

= 10

= - \frac{10}{10}

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

Apply trig inverse properties

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

General solutions for

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

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

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

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