What is the general solution for 1.33*sin(60)=1.52*sin(x) ?

The general solution for 1.33*sin(60)=1.52*sin(x) is x=0.85989…+360n,x=180-0.85989…+360n

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1.33sin(60)=1.52sin(x)

1.33 \cdot sin (6 0^{\circ}) = 1.52 \cdot sin (x)

x = 0.85989 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.85989 \dots + 36 0^{\circ} n

Radians

x = 0.85989 \dots + 2 πn, x = π - 0.85989 \dots + 2 πn

Solution steps

1.33 sin (6 0^{\circ}) = 1.52 sin (x)

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\circ})

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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}

= \frac{3}{2}

= \frac{3}{2}

1.33 \cdot \frac{3}{2} = 1.52 sin (x)

Switch sides

1.52 sin (x) = 1.33 \cdot \frac{3}{2}

Divide both sides by

1.52

1.52 sin (x) = 1.33 \cdot \frac{3}{2}

Divide both sides by

1.52

\frac{1.52 sin ( x )}{1.52} = \frac{1.33 \cdot \frac{3}{2}}{1.52}

Simplify

\frac{1.52 sin ( x )}{1.52} = \frac{1.33 \cdot \frac{3}{2}}{1.52}

Simplify

\frac{1.52 sin ( x )}{1.52} : sin (x)

\frac{1.52 sin ( x )}{1.52}

Cancel the common factor:

1.52

= sin (x)

Simplify

\frac{1.33 \cdot \frac{3}{2}}{1.52} : 0.75777 \dots

\frac{1.33 \cdot \frac{3}{2}}{1.52}

Multiply

1.33 \cdot \frac{3}{2} : 1.15181 \dots

1.33 \cdot \frac{3}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 \cdot 1.33}{2}

Convert element to a decimal form

3 = 1.73205 \dots

= \frac{1.73205 \dots \cdot 1.33}{2}

Multiply the numbers:

1.73205 \dots \cdot 1.33 = 2.30362 \dots

= \frac{2.30362 \dots}{2}

Divide the numbers:

\frac{2.30362 \dots}{2} = 1.15181 \dots

= 1.15181 \dots

= \frac{1.15181 \dots}{1.52}

Divide the numbers:

\frac{1.15181 \dots}{1.52} = 0.75777 \dots

= 0.75777 \dots

sin (x) = 0.75777 \dots

sin (x) = 0.75777 \dots

sin (x) = 0.75777 \dots

Apply trig inverse properties

sin (x) = 0.75777 \dots

General solutions for

sin (x) = 0.75777 \dots

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

x = arcsin (0.75777 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.75777 \dots) + 36 0^{\circ} n

x = arcsin (0.75777 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.75777 \dots) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.85989 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.85989 \dots + 36 0^{\circ} n

tan (x) = - 3 cos (x) tan (x)

tan (x - \frac{π}{4}) = \frac{1}{6}

csc (2 χ) = \frac{1}{1 - cos ( 2 χ )}

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

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

What is the general solution for 1.33*sin(60)=1.52*sin(x) ?
The general solution for 1.33*sin(60)=1.52*sin(x) is x=0.85989…+360n,x=180-0.85989…+360n