sin(a)=0.172

Take the inverse sine of both sides of the equation to extract a from inside the sine.

a=arcsin(0.172)

Evaluate arcsin(0.172).

a=0.17285956

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from π to find the solution in the second quadrant.

a=(3.14159265)-0.17285956

Remove the parentheses around the expression 3.14159265.

a=3.14159265-0.17285956

Subtract 0.17285956 from 3.14159265.

a=2.96873308

a=2.96873308

The period of the function can be calculated using 2π|b|.

2π|b|

Replace b with 1 in the formula for period.

2π|1|

Solve the equation.

The absolute value is the distance between a number and zero. The distance between 0 and 1 is 1.

2π1

Divide 2π by 1.

2π

2π

2π

The period of the sin(a) function is 2π so values will repeat every 2π radians in both directions.

a=0.17285956+2πn,2.96873308+2πn, for any integer n

Solve for a sin(a)=0.172