What is the general solution for sin(θ)= 33/55 ?

The general solution for sin(θ)= 33/55 is θ=0.64350…+2pin,θ=pi-0.64350…+2pin

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sin(θ)= 33/55

sin (θ) = \frac{33}{55}

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

Degrees

θ = 36.86989 \dots^{\circ} + 36 0^{\circ} n, θ = 143.13010 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) = \frac{33}{55}

Cancel the common factor:

11

sin (θ) = \frac{3}{5}

Apply trig inverse properties

sin (θ) = \frac{3}{5}

General solutions for

sin (θ) = \frac{3}{5}

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

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

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

Show solutions in decimal form

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

2 cos (x) - 4 = - 3

\frac{sin ( 2 x )}{sin ( \frac{7 π}{2} - x )} = 2

- 2 sec (θ) + 23 = 0, 0^{\circ} \leq θ \leq 36 0^{\circ}

cos (x + 1) = - \frac{2}{5}

4 cos (2 x) + 1 = 3

What is the general solution for sin(θ)= 33/55 ?
The general solution for sin(θ)= 33/55 is θ=0.64350…+2pin,θ=pi-0.64350…+2pin