What is the value of csc(-450) ?

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csc(-450)

csc (- 45 0^{\circ})

- 1

Solution steps

csc (- 45 0^{\circ})

Use the following property:

csc (- x) = - csc (x)

csc (- 45 0^{\circ}) = - csc (45 0^{\circ})

= - csc (45 0^{\circ})

csc (45 0^{\circ}) = csc (9 0^{\circ})

csc (45 0^{\circ})

Rewrite

45 0^{\circ}

36 0^{\circ} + 9 0^{\circ}

= csc (36 0^{\circ} + 9 0^{\circ})

Apply the periodicity of

csc

csc (x + 36 0^{\circ}) = csc (x)

csc (36 0^{\circ} + 9 0^{\circ}) = csc (9 0^{\circ})

= csc (9 0^{\circ})

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

Use the following trivial identity:

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

csc (9 0^{\circ})

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 1

= - 1

arccos (0.72)

arctan (\frac{10}{6})

arcsin (- \frac{2}{5})

arccos (0.13)

arccos (0.45)