What is the general solution for (sin(90)}{5.8}=\frac{sin(x))/5 ?

The general solution for (sin(90)}{5.8}=\frac{sin(x))/5 is x=1.03933…+360n,x=180-1.03933…+360n

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(sin(90)}{5.8}=\frac{sin(x))/5

\frac{sin ( 9 0 ^{\circ} )}{5.8} = \frac{sin ( x )}{5}

x = 1.03933 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.03933 \dots + 36 0^{\circ} n

Radians

x = 1.03933 \dots + 2 πn, x = π - 1.03933 \dots + 2 πn

Solution steps

\frac{sin ( 9 0 ^{\circ} )}{5.8} = \frac{sin ( x )}{5}

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

Use the following trivial identity:

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1

\frac{1}{5.8} = \frac{sin ( x )}{5}

Switch sides

\frac{sin ( x )}{5} = \frac{1}{5.8}

Multiply both sides by

5

\frac{sin ( x )}{5} = \frac{1}{5.8}

Multiply both sides by

5

\frac{5 sin ( x )}{5} = \frac{1 \cdot 5}{5.8}

Simplify

\frac{5 sin ( x )}{5} = \frac{1 \cdot 5}{5.8}

Simplify

\frac{5 sin ( x )}{5} : sin (x)

\frac{5 sin ( x )}{5}

Divide the numbers:

\frac{5}{5} = 1

= sin (x)

Simplify

\frac{1 \cdot 5}{5.8} : 0.86206 \dots

\frac{1 \cdot 5}{5.8}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5}{5.8}

Divide the numbers:

\frac{5}{5.8} = 0.86206 \dots

= 0.86206 \dots

sin (x) = 0.86206 \dots

sin (x) = 0.86206 \dots

sin (x) = 0.86206 \dots

Apply trig inverse properties

sin (x) = 0.86206 \dots

General solutions for

sin (x) = 0.86206 \dots

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

x = arcsin (0.86206 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.86206 \dots) + 36 0^{\circ} n

x = arcsin (0.86206 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.86206 \dots) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.03933 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.03933 \dots + 36 0^{\circ} n

sin (x) tan (x) + 3 sin (x) = 0

4 = 5 + 3 sin (2 t - \frac{π}{5})

sin^{2} (2 x) + 2 \cdot cos^{2} (x) - 2 = 0

tan (θ) = - 0.5586, 0 \leq θ < 2 π

6 cos^{2} (x) - sin (x) - 5 = 0, 0 \leq x \leq 2 π

What is the general solution for (sin(90)}{5.8}=\frac{sin(x))/5 ?
The general solution for (sin(90)}{5.8}=\frac{sin(x))/5 is x=1.03933…+360n,x=180-1.03933…+360n