What is the general solution for 1*sin(54.86)=2.451*sin(x) ?

The general solution for 1*sin(54.86)=2.451*sin(x) is x=0.34016…+360n,x=180-0.34016…+360n

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1sin(54.86)=2.451sin(x)

1 \cdot sin (54.8 6^{\circ}) = 2.451 \cdot sin (x)

x = 0.34016 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.34016 \dots + 36 0^{\circ} n

Radians

x = 0.34016 \dots + 2 πn, x = π - 0.34016 \dots + 2 πn

Solution steps

1 \cdot sin (54.8 6^{\circ}) = 2.451 sin (x)

Switch sides

2.451 sin (x) = 1 \cdot sin (54.8 6^{\circ})

Multiply:

1 \cdot sin (54.8 6^{\circ}) = sin (54.8 6^{\circ})

2.451 sin (x) = sin (54.8 6^{\circ})

Divide both sides by

2.451

2.451 sin (x) = sin (54.8 6^{\circ})

Divide both sides by

2.451

\frac{2.451 sin ( x )}{2.451} = \frac{sin ( 54.8 6 ^{\circ} )}{2.451}

Simplify

sin (x) = \frac{sin ( 54.8 6 ^{\circ} )}{2.451}

sin (x) = \frac{sin ( 54.8 6 ^{\circ} )}{2.451}

Apply trig inverse properties

sin (x) = \frac{sin ( 54.8 6 ^{\circ} )}{2.451}

General solutions for

sin (x) = \frac{sin ( 54.8 6 ^{\circ} )}{2.451}

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

x = arcsin (\frac{sin ( 54.8 6 ^{\circ} )}{2.451}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 54.8 6 ^{\circ} )}{2.451}) + 36 0^{\circ} n

x = arcsin (\frac{sin ( 54.8 6 ^{\circ} )}{2.451}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 54.8 6 ^{\circ} )}{2.451}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.34016 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.34016 \dots + 36 0^{\circ} n

\frac{cot ( θ )}{csc ( θ )} = sin (θ)

cos (t) = - \frac{2}{3}

sin (θ) = 1 + (1 - (cos (θ) - 1)^{2})

0 = 4 cos (4 x)

tan (θ) = \frac{8}{7}, π < θ < \frac{3 π}{2}

What is the general solution for 1*sin(54.86)=2.451*sin(x) ?
The general solution for 1*sin(54.86)=2.451*sin(x) is x=0.34016…+360n,x=180-0.34016…+360n