What is the general solution for sin(θ_{1})=-10/13 ?

The general solution for sin(θ_{1})=-10/13 is θ_{1}=-0.87763…+2pin,θ_{1}=pi+0.87763…+2pin

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sin(θ_{1})=-10/13

sin (θ_{1}) = - \frac{10}{13}

θ_{1} = - 0.87763 \dots + 2 πn, θ_{1} = π + 0.87763 \dots + 2 πn

Degrees

θ_{1} = - 50.28486 \dots^{\circ} + 36 0^{\circ} n, θ_{1} = 230.28486 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ_{1}) = - \frac{10}{13}

Apply trig inverse properties

sin (θ_{1}) = - \frac{10}{13}

General solutions for

sin (θ_{1}) = - \frac{10}{13}

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

θ_{1} = arcsin (- \frac{10}{13}) + 2 πn, θ_{1} = π + arcsin (\frac{10}{13}) + 2 πn

θ_{1} = arcsin (- \frac{10}{13}) + 2 πn, θ_{1} = π + arcsin (\frac{10}{13}) + 2 πn

Show solutions in decimal form

θ_{1} = - 0.87763 \dots + 2 πn, θ_{1} = π + 0.87763 \dots + 2 πn

sin (a^{- 1}) = \frac{2.6}{0.1733}

sin (θ) + cos (θ) = 0.46

3 cos (x) - 4 sin (x) = 5

cos (2 x) + 2 cos (x) = - 1

2 cos (x - \frac{π}{4}) - 1 = 0

What is the general solution for sin(θ_{1})=-10/13 ?
The general solution for sin(θ_{1})=-10/13 is θ_{1}=-0.87763…+2pin,θ_{1}=pi+0.87763…+2pin