What is the value of -(-10-16)/2 sin(-60)+(-5)cos(-60) ?

The value of -(-10-16)/2 sin(-60)+(-5)cos(-60) is (-13sqrt(3)-5)/2

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-(-10-16)/2 sin(-60)+(-5)cos(-60)

- \frac{- 10 - 16}{2} sin (- 6 0^{\circ}) + (- 5) cos (- 6 0^{\circ})

\frac{- 13 3 - 5}{2}

Decimal Notation

- 13.75833 \dots

Solution steps

- \frac{- 10 - 16}{2} sin (- 6 0^{\circ}) + (- 5) cos (- 6 0^{\circ})

Simplify

= 13 sin (- 6 0^{\circ}) - 5 cos (- 6 0^{\circ})

Use the following property:

cos (- x) = cos (x)

cos (- 6 0^{\circ}) = cos (6 0^{\circ})

= 13 sin (- 6 0^{\circ}) - 5 cos (6 0^{\circ})

Use the following property:

sin (- x) = - sin (x)

sin (- 6 0^{\circ}) = - sin (6 0^{\circ})

= 13 (- sin (6 0^{\circ})) - 5 cos (6 0^{\circ})

Simplify

= - 13 sin (6 0^{\circ}) - 5 cos (6 0^{\circ})

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\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{3}{2}

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 0^{\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{1}{2}

= - 13 \cdot \frac{3}{2} - 5 \cdot \frac{1}{2}

Simplify

- 13 \cdot \frac{3}{2} - 5 \cdot \frac{1}{2} : \frac{- 13 3 - 5}{2}

- 13 \cdot \frac{3}{2} - 5 \cdot \frac{1}{2}

13 \cdot \frac{3}{2} = \frac{13 3}{2}

13 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 13}{2}

5 \cdot \frac{1}{2} = \frac{5}{2}

5 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 5}{2}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5}{2}

= - \frac{13 3}{2} - \frac{5}{2}

Apply rule

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

= \frac{- 13 3 - 5}{2}

= \frac{- 13 3 - 5}{2}

sin (2.4)

200 \cdot cos (12 0^{\circ})

arctan (- \frac{π}{36})

150 \cdot cos (1 0^{\circ})

tan^{2} (4^{\circ}) + tan^{2} (2^{\circ})

What is the value of -(-10-16)/2 sin(-60)+(-5)cos(-60) ?
The value of -(-10-16)/2 sin(-60)+(-5)cos(-60) is (-13sqrt(3)-5)/2