What is the value of picos((5pi)/4)sin((5pi)/4) ?

The value of picos((5pi)/4)sin((5pi)/4) is picos((5pi)/4)sin((5pi)/4)

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picos((5pi)/4)sin((5pi)/4)

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

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

Decimal Notation

1.57079 \dots

Solution steps

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

Rewrite using trig identities:

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

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

Use the Double Angle identity:

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

sin (x) cos (x) = \frac{sin ( 2 x )}{2}

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

Simplify:

2 \cdot \frac{5 π}{4} = \frac{5 π}{2}

2 \cdot \frac{5 π}{4}

Multiply fractions:

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

= \frac{5 π 2}{4}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{10 π}{4}

Cancel the common factor:

2

= \frac{5 π}{2}

= \frac{sin ( \frac{5 π}{2} )}{2}

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

sin (\frac{5 π}{2})

Rewrite

\frac{5 π}{2}

2 π + \frac{π}{2}

= sin (2 π + \frac{π}{2})

Apply the periodicity of

sin

sin (x + 2 π) = sin (x)

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

= sin (\frac{π}{2})

= \frac{sin ( \frac{π}{2} )}{2}

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

\frac{1}{1 + cos ( \frac{π}{2} )}

80 \cdot 20 \cdot cos (3 0^{\circ})

sin (36.4 5^{\circ})

8 cos (1)

\frac{1}{π ^{2}} sin (π (1)) - \frac{( 1 ) cos ( π ( 1 ) )}{π}

What is the value of picos((5pi)/4)sin((5pi)/4) ?
The value of picos((5pi)/4)sin((5pi)/4) is picos((5pi)/4)sin((5pi)/4)