What is the value of csc((-pi)/2) ?

The value of csc((-pi)/2) is -1

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csc((-pi)/2)

csc (\frac{- π}{2})

- 1

Solution steps

csc (\frac{- π}{2})

Simplify

= csc (- \frac{π}{2})

Use the following property:

csc (- x) = - csc (x)

csc (- \frac{π}{2}) = - csc (\frac{π}{2})

= - csc (\frac{π}{2})

Use the following trivial identity:

csc (\frac{π}{2}) = 1

csc (\frac{π}{2})

csc (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 1

= - 1

sin (arcsin (\frac{8}{17}) + arccos (- \frac{3}{5}))

8 \cdot cos (4 0^{\circ})

1 - cos (\frac{π}{6})

6 cos (26 0^{\circ})

20 cos (7 5^{\circ})