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}

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})

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

Use the following trivial identity:

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

Use the following trivial identity:

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

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