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

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

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picos((3pi)/4)sin((3pi)/4)

π cos (\frac{3 π}{4}) sin (\frac{3 π}{4})

- \frac{π}{2}

Decimal Notation

- 1.57079 \dots

Solution steps

π cos (\frac{3 π}{4}) sin (\frac{3 π}{4})

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

cos (\frac{3 π}{4})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{2}{2}

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}

= π (- \frac{2}{2}) \frac{2}{2}

Simplify

π (- \frac{2}{2}) \frac{2}{2} : - \frac{π}{2}

π (- \frac{2}{2}) \frac{2}{2}

Remove parentheses:

(- a) = - a

= - π \frac{2}{2} \cdot \frac{2}{2}

Multiply fractions:

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

= - \frac{2 2 π}{2 \cdot 2}

22 π = 2 π

22 π

Apply radical rule:

a a = a

22 = 2

= 2 π

= - \frac{2 π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= - \frac{2 π}{4}

Cancel the common factor:

2

= - \frac{π}{2}

= - \frac{π}{2}

cot (6 7^{\circ})

sin (2 (0)) (0)

arccos (0.1423)

sin (12.47 4^{\circ})

cos (\frac{π}{11}) + cos (\frac{3 π}{11}) + cos (\frac{8 π}{11}) + cos (\frac{10 π}{11})

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