What is the value of 4sin(pi/8)cos(pi/8) ?

The value of 4sin(pi/8)cos(pi/8) is square root of 2

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4sin(pi/8)cos(pi/8)

4 sin (\frac{π}{8}) cos (\frac{π}{8})

2

Decimal Notation

1.41421 \dots

Solution steps

4 sin (\frac{π}{8}) cos (\frac{π}{8})

Rewrite using trig identities:

sin (\frac{π}{8}) cos (\frac{π}{8}) = \frac{sin ( \frac{π}{4} )}{2}

sin (\frac{π}{8}) cos (\frac{π}{8})

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{π}{8} )}{2}

Simplify:

2 \cdot \frac{π}{8} = \frac{π}{4}

2 \cdot \frac{π}{8}

Multiply fractions:

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

= \frac{π 2}{8}

Cancel the common factor:

2

= \frac{π}{4}

= \frac{sin ( \frac{π}{4} )}{2}

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

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

4 \cdot \frac{sin ( \frac{π}{4} )}{2}

Multiply fractions:

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

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

Divide the numbers:

\frac{4}{2} = 2

= 2 sin (\frac{π}{4})

= 2 sin (\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}

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

Simplify

2 \cdot \frac{2}{2} : 2

2 \cdot \frac{2}{2}

Multiply fractions:

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

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

Cancel the common factor:

2

= 2

= 2

sin (26 5^{\circ})

7 sin (6 0^{\circ})

arctan (\frac{8}{- 6})

6 cos (\frac{π}{6}) cos (\frac{π}{3})

cos (π (1))

What is the value of 4sin(pi/8)cos(pi/8) ?
The value of 4sin(pi/8)cos(pi/8) is square root of 2