What is the general solution for sin(x)=0.2174 ?

The general solution for sin(x)=0.2174 is x=0.21914…+2pin,x=pi-0.21914…+2pin

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sin(x)=0.2174

sin (x) = 0.2174

x = 0.21914 \dots + 2 πn, x = π - 0.21914 \dots + 2 πn

Degrees

x = 12.55636 \dots^{\circ} + 36 0^{\circ} n, x = 167.44363 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = 0.2174

Apply trig inverse properties

sin (x) = 0.2174

General solutions for

sin (x) = 0.2174

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

x = arcsin (0.2174) + 2 πn, x = π - arcsin (0.2174) + 2 πn

x = arcsin (0.2174) + 2 πn, x = π - arcsin (0.2174) + 2 πn

Show solutions in decimal form

x = 0.21914 \dots + 2 πn, x = π - 0.21914 \dots + 2 πn

x, arccot (x^{2}) y = arccot (x^{2})

\frac{50}{33} = \frac{sin ( x )}{sin ( 12 0 ^{\circ} - x )}

cot (x) csc (x) = cos (x)

2 tan (x) = 2

0.5 = cos (\frac{π}{6} x)

What is the general solution for sin(x)=0.2174 ?
The general solution for sin(x)=0.2174 is x=0.21914…+2pin,x=pi-0.21914…+2pin