What is the general solution for sin(θ)= 3/5 ,0<θ< pi/2 ?

The general solution for sin(θ)= 3/5 ,0<θ< pi/2 is θ=0.64350…

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sin(θ)= 3/5 ,0<θ< pi/2

sin (θ) = \frac{3}{5}, 0 < θ < \frac{π}{2}

θ = 0.64350 \dots

Degrees

θ = 36.86989 \dots^{\circ}

Solution steps

sin (θ) = \frac{3}{5}, 0 < θ < \frac{π}{2}

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

Solutions for the range

0 < θ < \frac{π}{2}

θ = arcsin (\frac{3}{5})

Show solutions in decimal form

θ = 0.64350 \dots

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

- 4 sin^{2} (θ) - 15 sin (θ) = - 7 sin (θ) - 5

tan^{2} (θ) + 7 tan (θ) + 5 = 0

tan (θ) = \frac{2 3}{1}

cos^{2} (x) - cos (x) = 0, x, 0 \leq x \leq 2 π

What is the general solution for sin(θ)= 3/5 ,0<θ< pi/2 ?
The general solution for sin(θ)= 3/5 ,0<θ< pi/2 is θ=0.64350…