What is the value of -cot(-pi/4) ?

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-cot(-pi/4)

- cot (- \frac{π}{4})

1

Solution steps

- cot (- \frac{π}{4})

Rewrite using trig identities:

cot (- \frac{π}{4}) = - 1

cot (- \frac{π}{4})

Use the following property:

cot (- x) = - cot (x)

cot (- \frac{π}{4}) = - cot (\frac{π}{4})

= - cot (\frac{π}{4})

Use the following trivial identity:

cot (\frac{π}{4}) = 1

cot (\frac{π}{4})

cot (x)

periodicity table with

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 1

= - 1

= - (- 1)

Simplify

= 1

- sin (3 π)

sec (3 2^{\circ})

arccsc (- 7)

arctan (\frac{4}{- 2})

sin (37. 5^{\circ})