What is the value of 6sin((5pi)/6) ?

The value of 6sin((5pi)/6) is 3

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6sin((5pi)/6)

6 sin (\frac{5 π}{6})

3

Solution steps

6 sin (\frac{5 π}{6})

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

sin (\frac{5 π}{6})

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}

= \frac{1}{2}

= 6 \cdot \frac{1}{2}

Simplify

6 \cdot \frac{1}{2} : 3

6 \cdot \frac{1}{2}

Convert element to fraction:

6 = \frac{6}{1}

= \frac{6}{1} \cdot \frac{1}{2}

Cross-cancel common factor:

2

= \frac{3}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 3

= 3

- cos (\frac{π}{4}) - (- cos (0))

cos (\frac{π}{4}) cos (\frac{π}{4}) - sin (\frac{π}{4}) sin (\frac{π}{4})

cos^{2} (3 0^{\circ}) + sin^{2} (3 0^{\circ})

\frac{15}{tan ( 3 0 ^{\circ} )}

sin (2) (50)