What is the value of 5sin((78pi)/(13)) ?

The value of 5sin((78pi)/(13)) is 0

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5sin((78pi)/(13))

5 sin (\frac{78 π}{13})

0

Solution steps

5 sin (\frac{78 π}{13})

Simplify

= 5 sin (6 π)

sin (6 π) = sin (0)

sin (6 π)

Rewrite

6 π

2 π \cdot 3 + 0

= sin (2 π 3 + 0)

Apply the periodicity of

sin

sin (x + 2 π \cdot k) = sin (x)

sin (2 π \cdot 3 + 0) = sin (0)

= sin (0)

= 5 sin (0)

Use the following trivial identity:

sin (0) = 0

sin (0)

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}

= 0

= 5 \cdot 0

Simplify

= 0

18 + 2 sin (5)

23.47 \cdot sin (\frac{360 ( 284 + 51 )}{365})

arccos (\frac{5}{13 26})

sin (2) π^{\circ}

e^{c o s (\frac{3 π}{2})}