What is the value of 22sin(pi/6) ?

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22sin(pi/6)

22 sin (\frac{π}{6})

11

Solution steps

22 sin (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{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}

= 22 \cdot \frac{1}{2}

Simplify

22 \cdot \frac{1}{2} : 11

22 \cdot \frac{1}{2}

Convert element to fraction:

22 = \frac{22}{1}

= \frac{1}{2} \cdot \frac{22}{1}

Cross-cancel common factor:

2

= \frac{11}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 11

= 11

sin (15 0^{\circ}) + tan (22 5^{\circ}) + cos (30 0^{\circ})

2 sin (\frac{- π}{4})

sin (1 1^{\circ}) cos (4 9^{\circ}) + cos (1 0^{\circ}) sin (4 9^{\circ})

sin (- 87 0^{\circ})

arctan (7272)