What is the value of 10sin(pi/6 5) ?

The value of 10sin(pi/6 5) is 5

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10sin(pi/6 5)

10 sin (\frac{π}{6} 5)

5

Solution steps

10 sin (\frac{π}{6} \cdot 5)

Rewrite using trig identities:

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

sin (\frac{π}{6} \cdot 5)

Simplify:

\frac{π}{6} \cdot 5 = \frac{5 π}{6}

\frac{π}{6} \cdot 5

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}

= 10 \cdot \frac{1}{2}

Simplify

10 \cdot \frac{1}{2} : 5

10 \cdot \frac{1}{2}

Convert element to fraction:

10 = \frac{10}{1}

= \frac{1}{2} \cdot \frac{10}{1}

Cross-cancel common factor:

2

= \frac{5}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 5

= 5

4 sin (\frac{1}{4}) - cos (\frac{1}{4})

sin (\frac{5}{6}) π

arcsin (cos (3 0^{\circ}))

\frac{π}{4} cos (\frac{π}{4})

tan (arccsc (2))