What is the general solution for sin(θ)=((-2/7))/2 ?

The general solution for sin(θ)=((-2/7))/2 is θ=-0.14334…+2pin,θ=pi+0.14334…+2pin

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sin(θ)=((-2/7))/2

sin (θ) = \frac{( - \frac{2}{7} )}{2}

θ = - 0.14334 \dots + 2 πn, θ = π + 0.14334 \dots + 2 πn

Radians

θ = - 0.14334 \dots + 6.28318 \dots n, θ = π + 0.14334 \dots + 6.28318 \dots n

Solution steps

sin (θ) = \frac{( - \frac{2}{7} )}{2}

Simplify

\frac{- \frac{2}{7}}{2} : - \frac{1}{7}

\frac{- \frac{2}{7}}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{\frac{2}{7}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

\frac{\frac{2}{7}}{2} = \frac{2}{7 \cdot 2}

= - \frac{2}{7 \cdot 2}

Multiply the numbers:

7 \cdot 2 = 14

= - \frac{2}{14}

Cancel the common factor:

2

= - \frac{1}{7}

Apply trig inverse properties

sin (θ) = - \frac{1}{7}

General solutions for

sin (θ) = - \frac{1}{7}

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

θ = arcsin (- \frac{1}{7}) + 2 πn, θ = π + arcsin (\frac{1}{7}) + 2 πn

θ = arcsin (- \frac{1}{7}) + 2 πn, θ = π + arcsin (\frac{1}{7}) + 2 πn

Show solutions in decimal form

θ = - 0.14334 \dots + 2 πn, θ = π + 0.14334 \dots + 2 πn

22 cos (θ) - 2 = 0

tan (x) = \frac{22}{326}

3 cos (6 x) = 2

2 cos (t) = 1 + sin (t)

cos (θ) = - \frac{5}{6}, csc (θ)

What is the general solution for sin(θ)=((-2/7))/2 ?
The general solution for sin(θ)=((-2/7))/2 is θ=-0.14334…+2pin,θ=pi+0.14334…+2pin