What is the value of -7sin(-pi/6) ?

The value of -7sin(-pi/6) is 7/2

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-7sin(-pi/6)

- 7 sin (- \frac{π}{6})

\frac{7}{2}

Decimal Notation

3.5

Solution steps

- 7 sin (- \frac{π}{6})

Rewrite using trig identities:

sin (- \frac{π}{6}) = - \frac{1}{2}

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}

= - 7 (- \frac{1}{2})

Simplify

- 7 (- \frac{1}{2}) : \frac{7}{2}

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

Apply rule

- (- a) = a

= 7 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 7}{2}

Multiply the numbers:

1 \cdot 7 = 7

= \frac{7}{2}

= \frac{7}{2}

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