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

The value of 6sin(pi/4)6cos(pi/4) is 18

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

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

18

Solution steps

6 sin (\frac{π}{4}) \cdot 6 cos (\frac{π}{4})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{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}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{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 \frac{2}{2} \cdot 6 \cdot \frac{2}{2}

Simplify

6 \cdot \frac{2}{2} \cdot 6 \cdot \frac{2}{2} : 18

6 \cdot \frac{2}{2} \cdot 6 \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 \cdot 6 \cdot 6}{2 \cdot 2}

22 \cdot 6 \cdot 6 = 72

22 \cdot 6 \cdot 6

Multiply the numbers:

6 \cdot 6 = 36

= 3622

Apply radical rule:

a a = a

22 = 2

= 36 \cdot 2

Multiply the numbers:

36 \cdot 2 = 72

= 72

= \frac{72}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{72}{4}

Divide the numbers:

\frac{72}{4} = 18

= 18

= 18

\frac{sin ( \frac{4 π}{3} ) cot ( \frac{5 π}{4} )}{cos ( \frac{π}{6} )}

8 \cdot csc (6 0^{\circ})

sin (\frac{π}{2} 5)

- sin (2 (\frac{π}{4}))

arccot (- 6)

What is the value of 6sin(pi/4)6cos(pi/4) ?
The value of 6sin(pi/4)6cos(pi/4) is 18