What is the general solution for -1=sin(4.18879x) ?

The general solution for -1=sin(4.18879x) is x=(3pi)/(8.37758)+(2pin)/(4.18879)

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-1=sin(4.18879x)

- 1 = sin (4.18879 x)

x = \frac{3 π}{8.37758} + \frac{2 πn}{4.18879}

Degrees

x = 64.45775 \dots^{\circ} + 85.94367 \dots^{\circ} n

Solution steps

- 1 = sin (4.18879 x)

Switch sides

sin (4.18879 x) = - 1

General solutions for

sin (4.18879 x) = - 1

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

4.18879 x = \frac{3 π}{2} + 2 πn

4.18879 x = \frac{3 π}{2} + 2 πn

Solve

4.18879 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{8.37758} + \frac{2 πn}{4.18879}

4.18879 x = \frac{3 π}{2} + 2 πn

Divide both sides by

4.18879

4.18879 x = \frac{3 π}{2} + 2 πn

Divide both sides by

4.18879

\frac{4.18879 x}{4.18879} = \frac{\frac{3 π}{2}}{4.18879} + \frac{2 πn}{4.18879}

Simplify

\frac{4.18879 x}{4.18879} = \frac{\frac{3 π}{2}}{4.18879} + \frac{2 πn}{4.18879}

Simplify

\frac{4.18879 x}{4.18879} : x

\frac{4.18879 x}{4.18879}

Cancel the common factor:

4.18879

= x

Simplify

\frac{\frac{3 π}{2}}{4.18879} + \frac{2 πn}{4.18879} : \frac{3 π}{8.37758} + \frac{2 πn}{4.18879}

\frac{\frac{3 π}{2}}{4.18879} + \frac{2 πn}{4.18879}

\frac{\frac{3 π}{2}}{4.18879} = \frac{3 π}{8.37758}

\frac{\frac{3 π}{2}}{4.18879}

Apply the fraction rule:

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

= \frac{3 π}{2 \cdot 4.18879}

Multiply the numbers:

2 \cdot 4.18879 = 8.37758

= \frac{3 π}{8.37758}

= \frac{3 π}{8.37758} + \frac{2 πn}{4.18879}

x = \frac{3 π}{8.37758} + \frac{2 πn}{4.18879}

x = \frac{3 π}{8.37758} + \frac{2 πn}{4.18879}

x = \frac{3 π}{8.37758} + \frac{2 πn}{4.18879}

x = \frac{3 π}{8.37758} + \frac{2 πn}{4.18879}

\frac{1}{sin ( x ) cos ( x )} = 22

tan (x) = \frac{1}{5 ^{\frac{1}{2}}}

3 csc (\frac{x}{2}) - 2 = 0

arcsin (y) = \frac{1}{2}

6 sin (y) = 0

What is the general solution for -1=sin(4.18879x) ?
The general solution for -1=sin(4.18879x) is x=(3pi)/(8.37758)+(2pin)/(4.18879)