What is the value of -sqrt(2)sin(pi/4) ?

The value of -sqrt(2)sin(pi/4) is -1

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-sqrt(2)sin(pi/4)

- 2 sin (\frac{π}{4})

- 1

Solution steps

- 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 \frac{2}{2}

Simplify

- 2 \frac{2}{2} : - 1

- 2 \frac{2}{2}

Multiply fractions:

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

= - \frac{2 2}{2}

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= - \frac{2}{2}

Apply rule

\frac{a}{a} = 1

= - 1

= - 1

2 sinh (0)

- csc (6 0^{\circ})

2 cos^{2} (4 8^{\circ}) - 1

sin (\frac{3 π}{5}) cos (\frac{4 π}{15}) - cos (\frac{3 π}{5}) sin (\frac{4 π}{15})

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