What is the general solution for sin(2θ)=0.9076 ?

The general solution for sin(2θ)=0.9076 is θ=(1.13753…)/2+pin,θ= pi/2-(1.13753…)/2+pin

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sin(2θ)=0.9076

sin (2 θ) = 0.9076

θ = \frac{1.13753 \dots}{2} + πn, θ = \frac{π}{2} - \frac{1.13753 \dots}{2} + πn

Degrees

θ = 32.58788 \dots^{\circ} + 18 0^{\circ} n, θ = 57.41211 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 θ) = 0.9076

Apply trig inverse properties

sin (2 θ) = 0.9076

General solutions for

sin (2 θ) = 0.9076

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

2 θ = arcsin (0.9076) + 2 πn, 2 θ = π - arcsin (0.9076) + 2 πn

2 θ = arcsin (0.9076) + 2 πn, 2 θ = π - arcsin (0.9076) + 2 πn

Solve

2 θ = arcsin (0.9076) + 2 πn : θ = \frac{arcsin ( 0.9076 )}{2} + πn

2 θ = arcsin (0.9076) + 2 πn

Divide both sides by

2

2 θ = arcsin (0.9076) + 2 πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{arcsin ( 0.9076 )}{2} + \frac{2 πn}{2}

Simplify

θ = \frac{arcsin ( 0.9076 )}{2} + πn

θ = \frac{arcsin ( 0.9076 )}{2} + πn

Solve

2 θ = π - arcsin (0.9076) + 2 πn : θ = \frac{π}{2} - \frac{arcsin ( 0.9076 )}{2} + πn

2 θ = π - arcsin (0.9076) + 2 πn

Divide both sides by

2

2 θ = π - arcsin (0.9076) + 2 πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{π}{2} - \frac{arcsin ( 0.9076 )}{2} + \frac{2 πn}{2}

Simplify

θ = \frac{π}{2} - \frac{arcsin ( 0.9076 )}{2} + πn

θ = \frac{π}{2} - \frac{arcsin ( 0.9076 )}{2} + πn

θ = \frac{arcsin ( 0.9076 )}{2} + πn, θ = \frac{π}{2} - \frac{arcsin ( 0.9076 )}{2} + πn

Show solutions in decimal form

θ = \frac{1.13753 \dots}{2} + πn, θ = \frac{π}{2} - \frac{1.13753 \dots}{2} + πn

7 sin (B) + 3 = sin (B) + 2

4 cos (x) = 3

cos (x + \frac{1}{6} π) cos (x - \frac{1}{6} π) = cos (2 x)

tan (\frac{a}{2}) = \frac{1}{2}

sin (x) = 0.731

What is the general solution for sin(2θ)=0.9076 ?
The general solution for sin(2θ)=0.9076 is θ=(1.13753…)/2+pin,θ= pi/2-(1.13753…)/2+pin