What is the value of sin(90)-sin(-90) ?

The value of sin(90)-sin(-90) is 2

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sin(90)-sin(-90)

sin (9 0^{\circ}) - sin (- 9 0^{\circ})

2

Solution steps

sin (9 0^{\circ}) - sin (- 9 0^{\circ})

Use the following property:

sin (- x) = - sin (x)

sin (- 9 0^{\circ}) = - sin (9 0^{\circ})

= sin (9 0^{\circ}) - (- sin (9 0^{\circ}))

Simplify

= 2 sin (9 0^{\circ})

Use the following trivial identity:

sin (9 0^{\circ}) = 1

sin (9 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}

= 1

= 2 \cdot 1

Simplify

= 2

2 cot (4 5^{\circ})

\frac{tan ( \frac{0.75 π}{2} )}{tan ( \frac{0.5 π}{2} )}

arccsch (2)

10 \cdot tan (4 0^{\circ})

sin (\frac{16 π}{1.4})