What is the value of 3+2sin((-pi)/6) ?

The value of 3+2sin((-pi)/6) is 2

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3+2sin((-pi)/6)

3 + 2 sin (\frac{- π}{6})

2

Solution steps

3 + 2 sin (\frac{- π}{6})

Rewrite using trig identities:

sin (\frac{- π}{6}) = - \frac{1}{2}

sin (\frac{- π}{6})

Simplify

= sin (- \frac{π}{6})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{π}{6}) = - sin (\frac{π}{6})

= - sin (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

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{1}{2}

= - \frac{1}{2}

= 3 + 2 (- \frac{1}{2})

Simplify

3 + 2 (- \frac{1}{2}) : 2

3 + 2 (- \frac{1}{2})

Remove parentheses:

(- a) = - a

= 3 - 2 \cdot \frac{1}{2}

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

2 \cdot \frac{1}{2}

Multiply fractions:

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

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

Cancel the common factor:

2

= 1

= 3 - 1

Subtract the numbers:

3 - 1 = 2

= 2

= 2

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