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Popular >

sin(13/2 pi)

Solution

sin (\frac{13}{2} π)

Solution

1

Solution steps

sin (\frac{13}{2} π)

Simplify:

\frac{13}{2} π = \frac{13 π}{2}

\frac{13}{2} π

Multiply fractions:

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

= \frac{13 π}{2}

= sin (\frac{13 π}{2})

sin (\frac{13 π}{2}) = sin (\frac{π}{2})

sin (\frac{13 π}{2})

Rewrite

\frac{13 π}{2}

as

2 π \cdot 3 + \frac{π}{2}

= sin (2 π 3 + \frac{π}{2})

Apply the periodicity of

sin

:

sin (x + 2 π \cdot k) = sin (x)

sin (2 π \cdot 3 + \frac{π}{2}) = sin (\frac{π}{2})

= sin (\frac{π}{2})

= sin (\frac{π}{2})

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

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}

= 1

= 1

Popular Examples

cos (3.1416)

-13.5cos(pi/6*45)+14.5

- 13.5 cos (\frac{π}{6} \cdot 45) + 14.5

(2(cos(pi/4)+isin(pi/4)))^3

(2 (cos (\frac{π}{4}) + i sin (\frac{π}{4})))^{3}

sin(arcsin(5/13)-arccos(-4/5))

sin (arcsin (\frac{5}{13}) - arccos (- \frac{4}{5}))

(250)/(cos(50))

\frac{250}{cos ( 5 0 ^{\circ} )}

Frequently Asked Questions (FAQ)

What is the value of sin(13/2 pi) ?
The value of sin(13/2 pi) is 1