What is the value of (sin(0.4*4*pi))/(pi*4) ?

The value of (sin(0.4*4*pi))/(pi*4) is (sin((8pi)/5))/(pi4)

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(sin(0.44pi))/(pi*4)

\frac{sin ( 0.4 \cdot 4 \cdot π )}{π \cdot 4}

\frac{sin ( \frac{8 π}{5} )}{π 4}

Decimal Notation

- 0.07568 \dots

Solution steps

\frac{sin ( 0.4 \cdot 4 π )}{π 4}

= \frac{sin ( \frac{2}{5} \cdot 4 π )}{π 4}

Rewrite as

= sin (2 \cdot \frac{4 π}{5})

Rewrite using trig identities:

sin (2 \cdot \frac{4 π}{5}) = 2 sin (\frac{4 π}{5}) cos (\frac{4 π}{5})

sin (2 \cdot \frac{4 π}{5})

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (\frac{4 π}{5}) cos (\frac{4 π}{5})

= \frac{sin ( \frac{2}{5} \cdot 4 π )}{π 4}

Simplify:

\frac{2}{5} \cdot 4 π = \frac{8 π}{5}

\frac{2}{5} \cdot 4 π

Multiply fractions:

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

= \frac{2 \cdot 4 π}{5}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{8 π}{5}

= \frac{sin ( \frac{8 π}{5} )}{π 4}

arctan (- 72705542)

csc^{2} (\frac{3 π}{2})

\frac{cos ( 1 ) - 1}{1}

sin^{2} (2 3^{\circ})

sec (60 0^{\circ}) + cot (31 5^{\circ})

What is the value of (sin(0.4*4*pi))/(pi*4) ?
The value of (sin(0.4*4*pi))/(pi*4) is (sin((8pi)/5))/(pi4)