What is the value of 3sin(45)-4tan(pi/6) ?

The value of 3sin(45)-4tan(pi/6) is (3sqrt(2))/2-(4sqrt(3))/3

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3sin(45)-4tan(pi/6)

3 sin (4 5^{\circ}) - 4 tan (\frac{π}{6})

\frac{3 2}{2} - \frac{4 3}{3}

Decimal Notation

- 0.18808 \dots

Solution steps

3 sin (4 5^{\circ}) - 4 tan (3 0^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\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{2}{2}

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}

= 3 \cdot \frac{2}{2} - 4 \cdot \frac{3}{3}

Simplify

3 \cdot \frac{2}{2} - 4 \cdot \frac{3}{3} : \frac{3 2}{2} - \frac{4 3}{3}

3 \cdot \frac{2}{2} - 4 \cdot \frac{3}{3}

Multiply

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

3 \cdot \frac{2}{2}

Multiply fractions:

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

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

= \frac{3 2}{2} - 4 \cdot \frac{3}{3}

Multiply

4 \cdot \frac{3}{3} : \frac{4 3}{3}

4 \cdot \frac{3}{3}

Multiply fractions:

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

= \frac{3 \cdot 4}{3}

= \frac{3 2}{2} - \frac{4 3}{3}

= \frac{3 2}{2} - \frac{4 3}{3}

cos (2 π) - cos (π)

tan (- 67 5^{\circ})

tan^{2} (1 2^{\circ})

cos (\frac{2 \cdot π}{3})

arctan (\frac{25}{10})

What is the value of 3sin(45)-4tan(pi/6) ?
The value of 3sin(45)-4tan(pi/6) is (3sqrt(2))/2-(4sqrt(3))/3