Question

Find the value of cot - 19 pi by 4

Answer 1

Answer:

$cot \frac{19\pi}{4} \\ = cot(4\pi + \frac{3\pi}{4} ) \\ = cot \frac{3\pi}{4} \\ = cot(\pi - \frac{\pi}{4} ) \\ = cot \frac{\pi}{4} \\ = - 1$

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Answer 2

Cot(-19/4) is the value of cot(19 pi by 4).

To make the expression simpler, we can use the identity shown below:

cot(x) = cos(x) / sin(x)

Substituting x =$-19π/4$, we get:

$cot(-19π/4)$ = $cos(-19π/4) / sin(-19π/4)$

To evaluate$cos(-19π/4) and sin(-19π/4)$, we can use the following identities:

cos(-θ) = cos(θ)

sin(-θ) = -sin(θ)

Using these identities, we have:

$cos(-19π/4) = cos(19π/4) = cos(4π + π/4) = cos(π/4) = 1/√2$

$sin(-19π/4) = -sin(19π/4) = -sin(4π + π/4) = -sin(π/4) = -1/√2$

When these values are used in place of the original expression, we obtain:

$cot(-19π/4) = cos(-19π/4) / sin(-19π/4) = (1/√2) / (-1/√2) = -1$

Therefore, $cot(-19π/4)$

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