What is the value of 6sin(pi/2)cos((3pi)/4) ?

The value of 6sin(pi/2)cos((3pi)/4) is -3sqrt(2)

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6sin(pi/2)cos((3pi)/4)

6 sin (\frac{π}{2}) cos (\frac{3 π}{4})

- 32

Decimal Notation

- 4.24264 \dots

Solution steps

6 sin (\frac{π}{2}) cos (\frac{3 π}{4})

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

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}

= 1

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}

= 6 \cdot 1 \cdot (- \frac{2}{2})

Simplify

6 \cdot 1 \cdot (- \frac{2}{2}) : - 32

6 \cdot 1 \cdot (- \frac{2}{2})

Remove parentheses:

(- a) = - a

= - 6 \cdot 1 \cdot \frac{2}{2}

Multiply fractions:

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

= - 1 \cdot \frac{6 2}{2}

Divide the numbers:

\frac{6}{2} = 3

= - 1 \cdot 32

Multiply the numbers:

1 \cdot 3 = 3

= - 32

= - 32

cos (\frac{9 π}{5})

csc (arcsin (\frac{3}{5}))

\frac{5}{cos ( 7 8 ^{\circ} )}

cos (\frac{π}{3} + π)

arccos (- \frac{1}{2})

What is the value of 6sin(pi/2)cos((3pi)/4) ?
The value of 6sin(pi/2)cos((3pi)/4) is -3sqrt(2)