What is the general solution for sin(2x)=0.35 ?

The general solution for sin(2x)=0.35 is x=(0.35757…)/2+pin,x= pi/2-(0.35757…)/2+pin

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sin(2x)=0.35

sin (2 x) = 0.35

x = \frac{0.35757 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.35757 \dots}{2} + πn

Degrees

x = 10.24365 \dots^{\circ} + 18 0^{\circ} n, x = 79.75634 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 x) = 0.35

Apply trig inverse properties

sin (2 x) = 0.35

General solutions for

sin (2 x) = 0.35

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

2 x = arcsin (0.35) + 2 πn, 2 x = π - arcsin (0.35) + 2 πn

2 x = arcsin (0.35) + 2 πn, 2 x = π - arcsin (0.35) + 2 πn

Solve

2 x = arcsin (0.35) + 2 πn : x = \frac{arcsin ( 0.35 )}{2} + πn

2 x = arcsin (0.35) + 2 πn

Divide both sides by

2

2 x = arcsin (0.35) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( 0.35 )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arcsin ( 0.35 )}{2} + πn

x = \frac{arcsin ( 0.35 )}{2} + πn

Solve

2 x = π - arcsin (0.35) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( 0.35 )}{2} + πn

2 x = π - arcsin (0.35) + 2 πn

Divide both sides by

2

2 x = π - arcsin (0.35) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( 0.35 )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} - \frac{arcsin ( 0.35 )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( 0.35 )}{2} + πn

x = \frac{arcsin ( 0.35 )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( 0.35 )}{2} + πn

Show solutions in decimal form

x = \frac{0.35757 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.35757 \dots}{2} + πn

2 cos (t) + sin (2 t) = 0

tan (θ) = cos (θ)

cos (x) = 0.766

cos (x) = \frac{sin ( x )}{2}

sin (θ) = - sin (θ) cos (θ)

What is the general solution for sin(2x)=0.35 ?
The general solution for sin(2x)=0.35 is x=(0.35757…)/2+pin,x= pi/2-(0.35757…)/2+pin