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

The general solution for sin(2θ)= 4/5 is θ=(0.92729…)/2+pin,θ= pi/2-(0.92729…)/2+pin

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sin(2θ)= 4/5

sin (2 θ) = \frac{4}{5}

θ = \frac{0.92729 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.92729 \dots}{2} + πn

Solution steps

sin (2 θ) = \frac{4}{5}

Apply trig inverse properties

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

Solve

2 θ = arcsin (\frac{4}{5}) + 2 πn : θ = \frac{arcsin ( \frac{4}{5} )}{2} + πn

Solve

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

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

Show solutions in decimal form

θ = \frac{0.92729 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.92729 \dots}{2} + πn

tan (2 x) = - 0.025

4 7^{\circ} = cos (x), x

cos (α) = \frac{7}{11}

x, m^{2} - m - 2 = sin (x)

2 sin^{2} (x) = sin (x) + 3, 0 \leq x \leq 2 π

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