What is the general solution for 0.04=0.08sin(x) ?

The general solution for 0.04=0.08sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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0.04=0.08sin(x)

0.04 = 0.08 sin (x)

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Degrees

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

0.04 = 0.08 sin (x)

Switch sides

0.08 sin (x) = 0.04

Multiply both sides by

100

0.08 sin (x) = 0.04

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

0.08 sin (x) \cdot 100 = 0.04 \cdot 100

Refine

8 sin (x) = 4

8 sin (x) = 4

Divide both sides by

8

8 sin (x) = 4

Divide both sides by

8

\frac{8 sin ( x )}{8} = \frac{4}{8}

Simplify

sin (x) = \frac{1}{2}

sin (x) = \frac{1}{2}

General solutions for

sin (x) = \frac{1}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

tan (x) = \frac{11}{18}

csc (A) \cdot tan (A) = sin (A)

cos (x) = \frac{2}{3}

(sec (3 x) - 2) (tan (2 x) - 1) = 0

cos (2 x) \cdot 2 - 2 cos (x) = 0

What is the general solution for 0.04=0.08sin(x) ?
The general solution for 0.04=0.08sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin