What is the value of sin(((3pi)/2)/(2)) ?

The value of sin(((3pi)/2)/(2)) is (sqrt(2))/2

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sin(((3pi)/2)/(2))

sin (\frac{\frac{3 π}{2}}{2})

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

sin (\frac{\frac{3 π}{2}}{2})

Simplify:

\frac{\frac{3 π}{2}}{2} = \frac{3 π}{4}

\frac{\frac{3 π}{2}}{2}

Apply the fraction rule:

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

= \frac{3 π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{3 π}{4}

= sin (\frac{3 π}{4})

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

sin (\frac{3 π}{4})

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{2}{2}

= \frac{2}{2}

arcsin (\frac{2}{9})

arccsc (4)

\frac{3}{tan ( 3 6 ^{\circ} )}

tan (7 6^{\circ})

sin (67 5^{\circ})

What is the value of sin(((3pi)/2)/(2)) ?
The value of sin(((3pi)/2)/(2)) is (sqrt(2))/2