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

The value of -1/2 sin(270)+2 is 5/2

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-1/2 sin(270)+2

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

\frac{5}{2}

Decimal Notation

2.5

Solution steps

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

Simplify

= \frac{- sin ( 27 0 ^{\circ} ) + 4}{2}

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{- 2 sin ( 13 5 ^{\circ} ) cos ( 13 5 ^{\circ} ) + 4}{2}

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 \cdot \frac{2}{2} ( - \frac{2}{2} ) + 4}{2}

Simplify

\frac{- 2 \cdot \frac{2}{2} ( - \frac{2}{2} ) + 4}{2} : \frac{5}{2}

\frac{- 2 \cdot \frac{2}{2} ( - \frac{2}{2} ) + 4}{2}

Apply rule

- (- a) = a

= \frac{2 \cdot \frac{2}{2} \cdot \frac{2}{2} + 4}{2}

2 \cdot \frac{2}{2} \cdot \frac{2}{2} = 1

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

Cancel the common factor:

2

= \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

= \frac{1 + 4}{2}

Add the numbers:

1 + 4 = 5

= \frac{5}{2}

= \frac{5}{2}

sin (\frac{23 π}{2})

coth (3)

\frac{sin ( 3 0 ^{\circ} )}{sin ( 20. 9 ^{\circ} )}

\frac{1}{2} arctan (\frac{1}{4})

arcsin (0.49969)