What is the general solution for sin(θ)= 1/3 ,0<θ< pi/2 ?

The general solution for sin(θ)= 1/3 ,0<θ< pi/2 is θ=0.33983…

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sin(θ)= 1/3 ,0<θ< pi/2

sin (θ) = \frac{1}{3}, 0 < θ < \frac{π}{2}

θ = 0.33983 \dots

Solution steps

sin (θ) = \frac{1}{3}, 0 < θ < \frac{π}{2}

Apply trig inverse properties

θ = arcsin (\frac{1}{3}) + 2 πn, θ = π - arcsin (\frac{1}{3}) + 2 πn

Solutions for the range

0 < θ < \frac{π}{2}

θ = arcsin (\frac{1}{3})

Show solutions in decimal form

θ = 0.33983 \dots

sec^{2} (x) + 2 sec (x) = 0

3 tan (\frac{θ + 11 π}{6}) = 3

8 cos^{2} (θ) + 13 = 14 cos (θ) + 8

cos (3 x) = - \frac{1}{2}, 0 \leq x < 2 π

cos (5 t) = 0

What is the general solution for sin(θ)= 1/3 ,0<θ< pi/2 ?
The general solution for sin(θ)= 1/3 ,0<θ< pi/2 is θ=0.33983…