What is the general solution for sin(θ)= 4/5 ,0<= θ<= pi/2 ?

The general solution for sin(θ)= 4/5 ,0<= θ<= pi/2 is θ=0.92729…

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sin(θ)= 4/5 ,0<= θ<= pi/2

sin (θ) = \frac{4}{5}, 0 \leq θ \leq \frac{π}{2}

θ = 0.92729 \dots

Degrees

θ = 53.13010 \dots^{\circ}

Solution steps

sin (θ) = \frac{4}{5}, 0 \leq θ \leq \frac{π}{2}

Apply trig inverse properties

sin (θ) = \frac{4}{5}

General solutions for

sin (θ) = \frac{4}{5}

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

θ = arcsin (\frac{4}{5}) + 2 πn, θ = π - arcsin (\frac{4}{5}) + 2 πn

θ = arcsin (\frac{4}{5}) + 2 πn, θ = π - arcsin (\frac{4}{5}) + 2 πn

Solutions for the range

0 \leq θ \leq \frac{π}{2}

θ = arcsin (\frac{4}{5})

Show solutions in decimal form

θ = 0.92729 \dots

- cos^{2} (x) + cos (x) + 2 = 0

2 - cos^{2} (x) = 4 sin^{2} (\frac{1}{2} x)

\frac{( tan ( x ) + 2 sin ( x ) )}{( tan ( x ) - 2 sin ( x ) )} = 3

sin^{(2)} (x) + cos (x) + 1 = 0

sin^{2} (θ) = 2 sin (θ)

What is the general solution for sin(θ)= 4/5 ,0<= θ<= pi/2 ?
The general solution for sin(θ)= 4/5 ,0<= θ<= pi/2 is θ=0.92729…