What is the value of 4sin(5*pi/6) ?

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4sin(5*pi/6)

4 sin (5 \cdot \frac{π}{6})

2

Solution steps

4 sin (5 \cdot \frac{π}{6})

Rewrite using trig identities:

sin (5 \cdot \frac{π}{6}) = \frac{1}{2}

sin (5 \cdot \frac{π}{6})

Simplify:

5 \cdot \frac{π}{6} = \frac{5 π}{6}

5 \cdot \frac{π}{6}

Multiply fractions:

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

= \frac{π 5}{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}

= \frac{1}{2}

= 4 \cdot \frac{1}{2}

Simplify

4 \cdot \frac{1}{2} : 2

4 \cdot \frac{1}{2}

Convert element to fraction:

4 = \frac{4}{1}

= \frac{4}{1} \cdot \frac{1}{2}

Cross-cancel common factor:

2

= \frac{2}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 2

= 2

tan (4 5^{\circ}) \cdot 5

4 cos (2 \cdot \frac{π}{2})

\frac{1}{sec ( \frac{π}{2} )}

arccos (- \frac{7}{15})

30 cos (7 0^{\circ})