What is the general solution for (sin(42)}{6.25}=\frac{sin(x))/9 ?

The general solution for (sin(42)}{6.25}=\frac{sin(x))/9 is x=1.29996…+360n,x=180-1.29996…+360n

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(sin(42)}{6.25}=\frac{sin(x))/9

\frac{sin ( 4 2 ^{\circ} )}{6.25} = \frac{sin ( x )}{9}

x = 1.29996 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.29996 \dots + 36 0^{\circ} n

Radians

x = 1.29996 \dots + 2 πn, x = π - 1.29996 \dots + 2 πn

Solution steps

\frac{sin ( 4 2 ^{\circ} )}{6.25} = \frac{sin ( x )}{9}

Switch sides

\frac{sin ( x )}{9} = \frac{sin ( 4 2 ^{\circ} )}{6.25}

Multiply both sides by

9

\frac{sin ( x )}{9} = \frac{sin ( 4 2 ^{\circ} )}{6.25}

Multiply both sides by

9

\frac{9 sin ( x )}{9} = \frac{9 sin ( 4 2 ^{\circ} )}{6.25}

Simplify

sin (x) = \frac{9 sin ( 4 2 ^{\circ} )}{6.25}

sin (x) = \frac{9 sin ( 4 2 ^{\circ} )}{6.25}

Apply trig inverse properties

sin (x) = \frac{9 sin ( 4 2 ^{\circ} )}{6.25}

General solutions for

sin (x) = \frac{9 sin ( 4 2 ^{\circ} )}{6.25}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{9 sin ( 4 2 ^{\circ} )}{6.25}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{9 sin ( 4 2 ^{\circ} )}{6.25}) + 36 0^{\circ} n

x = arcsin (\frac{9 sin ( 4 2 ^{\circ} )}{6.25}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{9 sin ( 4 2 ^{\circ} )}{6.25}) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.29996 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.29996 \dots + 36 0^{\circ} n

\frac{tan ( x ) + cot ( x )}{csc ( x )} = cos (x)

tan (θ) = - \frac{3}{7}

sin (2 x) = 0, - π \leq x \leq π

cos (2 x) - sin (2 x) = 1

2 cos (θ) = 3 cos (3 θ)

What is the general solution for (sin(42)}{6.25}=\frac{sin(x))/9 ?
The general solution for (sin(42)}{6.25}=\frac{sin(x))/9 is x=1.29996…+360n,x=180-1.29996…+360n