What is the general solution for 30=arccos(6/(x(3))) ?

The general solution for 30=arccos(6/(x(3))) is x= 4/(sqrt(3))

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30=arccos(6/(x(3)))

Solution

3 0^{\circ} = arccos (\frac{6}{x ( 3 )})

Solution

x = \frac{4}{3}

Solution steps

3 0^{\circ} = arccos (\frac{6}{x ( 3 )})

Switch sides

arccos (\frac{6}{x \cdot 3}) = 3 0^{\circ}

Apply trig inverse properties

arccos (\frac{6}{x \cdot 3}) = 3 0^{\circ}

arccos (x) = a \Rightarrow x = cos (a)

\frac{6}{x \cdot 3} = cos (3 0^{\circ})

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

cos (3 0^{\circ})

Use the following trivial identity:

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

cos (3 0^{\circ})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= \frac{3}{2}

\frac{6}{x \cdot 3} = \frac{3}{2}

\frac{6}{x \cdot 3} = \frac{3}{2}

Solve

\frac{6}{x \cdot 3} = \frac{3}{2} : x = \frac{4}{3}

\frac{6}{x \cdot 3} = \frac{3}{2}

Cross multiply

\frac{6}{x \cdot 3} = \frac{3}{2}

Simplify

\frac{6}{x \cdot 3} : \frac{2}{x}

\frac{6}{x \cdot 3}

Factor the number:

6 = 3 \cdot 2

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

Cancel the common factor:

3

= \frac{2}{x}

\frac{2}{x} = \frac{3}{2}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

2 \cdot 2 = x 3

Simplify

2 \cdot 2 : 4

2 \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 4

4 = x 3

4 = x 3

Switch sides

x 3 = 4

Divide both sides by

3

x 3 = 4

Divide both sides by

3

\frac{x 3}{3} = \frac{4}{3}

Simplify

x = \frac{4}{3}

x = \frac{4}{3}

Verify Solutions

Find undefined (singularity) points:

x = 0

Take the denominator(s) of

\frac{6}{x 3}

and compare to zero

Solve

x 3 = 0 : x = 0

x \cdot 3 = 0

Divide both sides by

3

x \cdot 3 = 0

Divide both sides by

3

\frac{x \cdot 3}{3} = \frac{0}{3}

Simplify

x = 0

x = 0

The following points are undefined

x = 0

Combine undefined points with solutions:

x = \frac{4}{3}

x = \frac{4}{3}

Popular Examples

sin(θ)=0.18421

sin (θ) = 0.18421

6/(3tan(θ)+1)=5

\frac{6}{3 tan ( θ ) + 1} = 5

cos(x)=2-3sin(x)

cos (x) = 2 - 3 sin (x)

tan(x/2)=1,5

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

2cos^2(x)-1-cos(x)=0,0<= x<= 2pi

2 cos^{2} (x) - 1 - cos (x) = 0, 0 \leq x \leq 2 π

Frequently Asked Questions (FAQ)

What is the general solution for 30=arccos(6/(x(3))) ?
The general solution for 30=arccos(6/(x(3))) is x= 4/(sqrt(3))