What is the value of sin(((3pi))/4) ?

The value of sin(((3pi))/4) is (sqrt(2))/2

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Find the Exact Value sin((3pi)/4)

sin (\frac{( 3 π )}{4})

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

sin (\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}

cos (\frac{( 3 π )}{2})

x, cos (x) = \frac{( 3 )}{2}

sec (x) = \frac{1}{( cos ( x ) )}

tan (0^{\circ})

sin (θ) = \frac{15}{17}, cos (θ) = \frac{8}{17}

What is the value of sin(((3pi))/4) ?
The value of sin(((3pi))/4) is (sqrt(2))/2