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

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

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-2sin(3/4 pi)

- 2 sin (\frac{3}{4} π)

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

- 2 sin (\frac{3}{4} π)

Rewrite using trig identities:

sin (\frac{3}{4} π) = \frac{2}{2}

sin (\frac{3}{4} π)

Simplify:

\frac{3}{4} π = \frac{3 π}{4}

\frac{3}{4} π

Multiply fractions:

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

= \frac{3 π}{4}

= sin (\frac{3 π}{4})

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}

= \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

sec (6 0^{\circ}) + sin (3 0^{\circ})

arcsin (sin (\frac{37 π}{5}))

arcsin (- 0.79)

1.06 \cdot sin (3 5^{\circ})

cos (1.24)