What is the value of sin((12pi)/4) ?

The value of sin((12pi)/4) is 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin((12pi)/4)

sin (\frac{12 π}{4})

0

Solution steps

sin (\frac{12 π}{4})

Simplify

= sin (3 π)

sin (3 π) = sin (π)

sin (3 π)

Rewrite

3 π

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

tan (\frac{1}{3} π)

sin^{3} (4 5^{\circ})

400 cos (2 0^{\circ})

6 cos (\frac{4 π}{3})

\frac{7.35 \cdot sin ( 7 5 ^{\circ} )}{sin ( 3 5 ^{\circ} )}