What is the value of cot(-(15pi)/8) ?

The value of cot(-(15pi)/8) is sqrt(2)+1

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cot(-(15pi)/8)

cot (- \frac{15 π}{8})

2 + 1

Solution steps

cot (- \frac{15 π}{8})

Use the following property:

cot (- x) = - cot (x)

cot (- \frac{15 π}{8}) = - cot (\frac{15 π}{8})

= - cot (\frac{15 π}{8})

cot (\frac{15 π}{8}) = cot (\frac{7 π}{8})

= - cot (\frac{7 π}{8})

Rewrite using trig identities:

cot (\frac{7 π}{8}) = - 2 - 1

= - (- 2 - 1)

Simplify

= 2 + 1

50 cos (0)

5 sin (15 0^{\circ})

arcsin (sin (- \frac{3 π}{7}))

\frac{- sin ( \frac{π}{2} )}{- cos ( \frac{π}{2} )}

arctan (\frac{7}{- 4})