What is the value of csc(-45) ?

The value of csc(-45) is -sqrt(2)

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csc(-45)

csc (- 4 5^{\circ})

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

csc (- 4 5^{\circ})

Use the following property:

csc (- x) = - csc (x)

csc (- 4 5^{\circ}) = - csc (4 5^{\circ})

= - csc (4 5^{\circ})

Use the following trivial identity:

csc (4 5^{\circ}) = 2

csc (4 5^{\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

= 2

= - 2

tan (- 2 π)

\frac{tan ( 2 0 ^{\circ} ) + tan ( 2 5 ^{\circ} )}{1 - tan ( 2 0 ^{\circ} ) tan ( 2 5 ^{\circ} )}

sin (1.5)

4 cos (2 π)

sec (\frac{8 π}{3})