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Popular >

sin(3*pi)

Solution

sin (3 \cdot π)

Solution

0

Solution steps

sin (3 π)

sin (3 π) = sin (π)

sin (3 π)

Rewrite

3 π

as

2 π + π

= sin (2 π + π)

Apply the periodicity of

sin

:

sin (x + 2 π) = sin (x)

sin (2 π + π) = sin (π)

= sin (π)

= sin (π)

Use the following trivial identity:

sin (π) = 0

sin (π)

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

= 0

Popular Examples

arctan (- 1.4)

cot (7 0^{\circ})

300 sin (6 0^{\circ})

arcsin(sin(pi/2))

arcsin (sin (\frac{π}{2}))

arccos(1/(sqrt(2)\sqrt{29)})

arccos (\frac{1}{2 29})

Frequently Asked Questions (FAQ)

What is the value of sin(3*pi) ?
The value of sin(3*pi) is 0