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

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-sin(-90)

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

1

Solution steps

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

Rewrite using trig identities:

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

sin (- 9 0^{\circ})

Use the following property:

sin (- x) = - sin (x)

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

= - 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

= - 1

= - (- 1)

Simplify

= 1

cos (arcsin (\frac{8}{17}))

arccos (\frac{6}{11})

3 cos (4 7^{\circ})

arcsin (\frac{1}{1.8})

csc (\frac{- 4 π}{3})