What is the value of -1/2 sin(270) ?

The value of -1/2 sin(270) is 1/2

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-1/2 sin(270)

- \frac{1}{2} sin (27 0^{\circ})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

- \frac{1}{2} sin (27 0^{\circ})

Rewrite using trig identities:

sin (27 0^{\circ}) = 2 sin (13 5^{\circ}) cos (13 5^{\circ})

sin (27 0^{\circ})

Write

sin (27 0^{\circ})

sin (2 \cdot 13 5^{\circ})

= sin (2 \cdot 13 5^{\circ})

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (13 5^{\circ}) cos (13 5^{\circ})

= - \frac{1}{2} \cdot 2 sin (13 5^{\circ}) cos (13 5^{\circ})

Simplify

= - sin (13 5^{\circ}) cos (13 5^{\circ})

Use the following trivial identity:

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} 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 (13 5^{\circ}) = - \frac{2}{2}

cos (13 5^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} 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}

= - \frac{2}{2} (- \frac{2}{2})

Simplify

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

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

Apply rule

- (- a) = a

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

Multiply fractions:

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

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

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{2}{4}

Cancel the common factor:

2

= \frac{1}{2}

= \frac{1}{2}

sin (42.3 1^{\circ})

csc (8 5^{\circ})

arccos (\frac{- 2}{29 26})

cos^{2} (\frac{π}{3}) + \frac{1}{2}

2 (0) - cos (0) + sin (0) + 0