What is the general solution for 39.2sin(x)=22.07 ?

The general solution for 39.2sin(x)=22.07 is x=0.59802…+2pin,x=pi-0.59802…+2pin

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39.2sin(x)=22.07

39.2 sin (x) = 22.07

x = 0.59802 \dots + 2 πn, x = π - 0.59802 \dots + 2 πn

Degrees

x = 34.26423 \dots^{\circ} + 36 0^{\circ} n, x = 145.73576 \dots^{\circ} + 36 0^{\circ} n

Solution steps

39.2 sin (x) = 22.07

Multiply both sides by

100

39.2 sin (x) = 22.07

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

39.2 sin (x) \cdot 100 = 22.07 \cdot 100

Refine

3920 sin (x) = 2207

3920 sin (x) = 2207

Divide both sides by

3920

3920 sin (x) = 2207

Divide both sides by

3920

\frac{3920 sin ( x )}{3920} = \frac{2207}{3920}

Simplify

sin (x) = \frac{2207}{3920}

sin (x) = \frac{2207}{3920}

Apply trig inverse properties

sin (x) = \frac{2207}{3920}

General solutions for

sin (x) = \frac{2207}{3920}

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

x = arcsin (\frac{2207}{3920}) + 2 πn, x = π - arcsin (\frac{2207}{3920}) + 2 πn

x = arcsin (\frac{2207}{3920}) + 2 πn, x = π - arcsin (\frac{2207}{3920}) + 2 πn

Show solutions in decimal form

x = 0.59802 \dots + 2 πn, x = π - 0.59802 \dots + 2 πn

tan (X) = 9.5144

cos (u) = \frac{3 π}{4}, sin (2 u)

cos (x) = \frac{- \frac{1}{2} ( 0.5 ) ( 9 )}{( 0.8 ) ( 0.5 ) ( 9.8 )}

cos (2 a) = \frac{31}{81}

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

What is the general solution for 39.2sin(x)=22.07 ?
The general solution for 39.2sin(x)=22.07 is x=0.59802…+2pin,x=pi-0.59802…+2pin