What is the general solution for 0.3=sin(9x) ?

The general solution for 0.3=sin(9x) is x=(0.30469…)/9+(2pin)/9 ,x= pi/9-(0.30469…)/9+(2pin)/9

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0.3=sin(9x)

0.3 = sin (9 x)

x = \frac{0.30469 \dots}{9} + \frac{2 πn}{9}, x = \frac{π}{9} - \frac{0.30469 \dots}{9} + \frac{2 πn}{9}

Solution steps

0.3 = sin (9 x)

Switch sides

sin (9 x) = 0.3

Apply trig inverse properties

9 x = arcsin (0.3) + 2 πn, 9 x = π - arcsin (0.3) + 2 πn

Solve

9 x = arcsin (0.3) + 2 πn : x = \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}

Solve

9 x = π - arcsin (0.3) + 2 πn : x = \frac{π}{9} - \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}

x = \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}, x = \frac{π}{9} - \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}

Show solutions in decimal form

x = \frac{0.30469 \dots}{9} + \frac{2 πn}{9}, x = \frac{π}{9} - \frac{0.30469 \dots}{9} + \frac{2 πn}{9}

sin (7 x) = cos (2 x)

cos^{2} (x) = cot (x) sin (x)

sec^{2} (x) csc (x) - 2 csc (x) = 2 - sec^{2} (x)

2 sin (x) = - 2, 0 \leq x \leq 2 π

csc (a) = 3

What is the general solution for 0.3=sin(9x) ?
The general solution for 0.3=sin(9x) is x=(0.30469…)/9+(2pin)/9 ,x= pi/9-(0.30469…)/9+(2pin)/9