What is the value of 440tan(30) ?

The value of 440tan(30) is (440sqrt(3))/3

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440tan(30)

440 tan (3 0^{\circ})

\frac{440 3}{3}

Decimal Notation

254.03411 \dots

Solution steps

440 tan (3 0^{\circ})

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

periodicity table with

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

= \frac{3}{3}

= 440 \cdot \frac{3}{3}

Simplify

440 \cdot \frac{3}{3} : \frac{440 3}{3}

440 \cdot \frac{3}{3}

Multiply fractions:

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

= \frac{3 \cdot 440}{3}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{440 \cdot 3 ^{\frac{1}{2}}}{3}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{440}{3 ^{1 - \frac{1}{2}}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{440}{3 ^{\frac{1}{2}}}

Apply radical rule:

3^{\frac{1}{2}} = 3

= \frac{440}{3}

Rationalize

\frac{440}{3} : \frac{440 3}{3}

\frac{440}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{440 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{440 3}{3}

= \frac{440 3}{3}

= \frac{440 3}{3}

csc (arctan (\frac{15}{8}))

125 tan (4 5^{\circ})

3 (cos (4 5^{\circ}) + i sin (4 5^{\circ})) \cdot 2 (cos (13 5^{\circ}) + i sin (13 5^{\circ}))

sin (π) cos (\frac{2 π}{5}) - cos (π) sin (\frac{2 π}{5})

25 cos (2 0^{\circ})