Question

Find the value of cot (-3155°)

Answer 1

Answer:

$\bf\:cot(-3155^{\circ})=tan5^{\circ}$

Step-by-step explanation:

Find the value of cot (-3155°)

$cot(-3155^{\circ})$

Using

$\boxed{cot(-\theta)=-cot\theta}$

$=-cot(3155^{\circ})$

$=-cot(8\times\:360^{\circ}+275^{\circ})$

$=-cot(270^{\circ}+5^{\circ})$

Using,

$\boxed{cot(270^{\circ}+\theta)=-tan\theta}$

$=-(-tan5^{\circ})$

$=tan5^{\circ}$

$\implies\:\bf\:cot(-3155^{\circ})=tan5^{\circ}$

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

cot (-3155°)

CALCULATION

STEP : 1

$\sf{Cot \theta \: \: is \: an \: odd \: function \: }$

$\sf{Cot ( - {3155}^{ \circ} }) = - \: Cot \: {3155}^{ \circ}$

STEP : 2

$\sf{ {3155}^{ \circ} } = 35 \times {90}^{ \circ} + {5}^{ \circ}$

So

$\sf{Cot ( - {3155}^{ \circ} })$

$\sf{= - \: Cot \: {3155}^{ \circ} }$

$\sf{= - \: Cot (\:35 \times {90}^{ \circ} + {5}^{ \circ}})$

STEP : 3

$\sf{ \:The \: angle \: {3155}^{ \circ} \: is \: in \: Fourth \: Quadrant \: }$

STEP : 4

35 is an odd natural number

RESULT

$\sf{Cot ( - {3155}^{ \circ} })$

$\sf{= - \: Cot (\:35 \times {90}^{ \circ} + {5}^{ \circ}})$

$\sf{= \: tan \: {5}^{ \circ}}$

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