What is the general solution for 60*pi/(180)=2arctan(x/(17)) ?

The general solution for 60*pi/(180)=2arctan(x/(17)) is x=(17)/(sqrt(3))

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60*pi/(180)=2arctan(x/(17))

Solution

60 \cdot \frac{π}{180} = 2 arctan (\frac{x}{17})

Solution

x = \frac{17}{3}

Solution steps

60 \cdot \frac{π}{180} = 2 arctan (\frac{x}{17})

Switch sides

2 arctan (\frac{x}{17}) = 60 \cdot \frac{π}{180}

Divide both sides by

2

2 arctan (\frac{x}{17}) = 60 \cdot \frac{π}{180}

Divide both sides by

2

\frac{2 arctan ( \frac{x}{17} )}{2} = \frac{60 \cdot \frac{π}{180}}{2}

Simplify

\frac{2 arctan ( \frac{x}{17} )}{2} = \frac{60 \cdot \frac{π}{180}}{2}

Simplify

\frac{2 arctan ( \frac{x}{17} )}{2} : arctan (\frac{x}{17})

\frac{2 arctan ( \frac{x}{17} )}{2}

Divide the numbers:

\frac{2}{2} = 1

= arctan (\frac{x}{17})

Simplify

\frac{60 \cdot \frac{π}{180}}{2} : \frac{π}{6}

\frac{60 \cdot \frac{π}{180}}{2}

Multiply

60 \cdot \frac{π}{180} : \frac{π}{3}

60 \cdot \frac{π}{180}

Multiply fractions:

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

= \frac{π 60}{180}

Cancel the common factor:

60

= \frac{π}{3}

= \frac{\frac{π}{3}}{2}

Apply the fraction rule:

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

= \frac{π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{π}{6}

arctan (\frac{x}{17}) = \frac{π}{6}

arctan (\frac{x}{17}) = \frac{π}{6}

arctan (\frac{x}{17}) = \frac{π}{6}

Apply trig inverse properties

arctan (\frac{x}{17}) = \frac{π}{6}

arctan (x) = a \Rightarrow x = tan (a)

\frac{x}{17} = tan (\frac{π}{6})

tan (\frac{π}{6}) = \frac{3}{3}

tan (\frac{π}{6})

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

tan (\frac{π}{6})

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= \frac{3}{3}

\frac{x}{17} = \frac{3}{3}

\frac{x}{17} = \frac{3}{3}

Solve

\frac{x}{17} = \frac{3}{3} : x = \frac{17}{3}

\frac{x}{17} = \frac{3}{3}

Apply radical rule:

a = a a

3 = 33

\frac{x}{17} = \frac{3}{3 3}

Cancel the common factor:

3

\frac{x}{17} = \frac{1}{3}

Multiply both sides by

17

\frac{x}{17} = \frac{1}{3}

Multiply both sides by

17

\frac{17 x}{17} = \frac{1 \cdot 17}{3}

Simplify

\frac{17 x}{17} = \frac{1 \cdot 17}{3}

Simplify

\frac{17 x}{17} : x

\frac{17 x}{17}

Divide the numbers:

\frac{17}{17} = 1

= x

Simplify

\frac{1 \cdot 17}{3} : \frac{17}{3}

\frac{1 \cdot 17}{3}

Multiply the numbers:

1 \cdot 17 = 17

= \frac{17}{3}

x = \frac{17}{3}

x = \frac{17}{3}

x = \frac{17}{3}

x = \frac{17}{3}

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Frequently Asked Questions (FAQ)

What is the general solution for 60*pi/(180)=2arctan(x/(17)) ?
The general solution for 60*pi/(180)=2arctan(x/(17)) is x=(17)/(sqrt(3))