What is the value of sin(60)-sin(-60) ?

The value of sin(60)-sin(-60) is square root of 3

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sin(60)-sin(-60)

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

3

Decimal Notation

1.73205 \dots

Solution steps

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

Use the following property:

sin (- x) = - sin (x)

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

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

Simplify

= 2 sin (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}

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

Simplify

2 \cdot \frac{3}{2} : 3

2 \cdot \frac{3}{2}

Multiply fractions:

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

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

Cancel the common factor:

2

= 3

= 3

36 \cdot cos (14 4^{\circ})

18 \cdot sin (72. 4^{\circ})

4 cos (0) - e^{0}

cos (3 0^{\circ}) \cdot 80

cos ((4 + \frac{50}{60} + \frac{15}{3600})^{\circ})

What is the value of sin(60)-sin(-60) ?
The value of sin(60)-sin(-60) is square root of 3