What is the general solution for sin(2x)=0.89583 ?

The general solution for sin(2x)=0.89583 is x=(1.11029…)/2+pin,x= pi/2-(1.11029…)/2+pin

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sin(2x)=0.89583

sin (2 x) = 0.89583

x = \frac{1.11029 \dots}{2} + πn, x = \frac{π}{2} - \frac{1.11029 \dots}{2} + πn

Degrees

x = 31.80762 \dots^{\circ} + 18 0^{\circ} n, x = 58.19237 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 x) = 0.89583

Apply trig inverse properties

sin (2 x) = 0.89583

General solutions for

sin (2 x) = 0.89583

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

2 x = arcsin (0.89583) + 2 πn, 2 x = π - arcsin (0.89583) + 2 πn

2 x = arcsin (0.89583) + 2 πn, 2 x = π - arcsin (0.89583) + 2 πn

Solve

2 x = arcsin (0.89583) + 2 πn : x = \frac{arcsin ( 0.89583 )}{2} + πn

2 x = arcsin (0.89583) + 2 πn

Divide both sides by

2

2 x = arcsin (0.89583) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( 0.89583 )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arcsin ( 0.89583 )}{2} + πn

x = \frac{arcsin ( 0.89583 )}{2} + πn

Solve

2 x = π - arcsin (0.89583) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( 0.89583 )}{2} + πn

2 x = π - arcsin (0.89583) + 2 πn

Divide both sides by

2

2 x = π - arcsin (0.89583) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( 0.89583 )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} - \frac{arcsin ( 0.89583 )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( 0.89583 )}{2} + πn

x = \frac{arcsin ( 0.89583 )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( 0.89583 )}{2} + πn

Show solutions in decimal form

x = \frac{1.11029 \dots}{2} + πn, x = \frac{π}{2} - \frac{1.11029 \dots}{2} + πn

tan (θ) = 1.234, θ

x, sin (x) cos (x) = sin (x + p) cos (x + p)

sin (θ) = \frac{3}{5}, cos (2 θ)

1 1^{2} = 6^{2} + 7^{2} - 2 \cdot 6 \cdot 7 \cdot cos (x)

2 cos^{2} (x) + cos (x) = 1, 0 \leq x \leq 2 π

What is the general solution for sin(2x)=0.89583 ?
The general solution for sin(2x)=0.89583 is x=(1.11029…)/2+pin,x= pi/2-(1.11029…)/2+pin