If tan 0= -(3)/(8), which expression is equivalent to cot 0 ?

Question

asked Mar 11, 2019 52.1k views

2 Answers

Acvcu · Answer 1 · 2019-03-12T09:35:45+0000

tan x = sin x / cos x

cot x = cos x/ sin x

We can see that tan and cot are reciprocal.

So, if tan(O) = -(3)/(8), then cot(O) = - (8)/3.

Romanski · Answer 2 · 2019-03-17T20:33:23+0000

Hence, the answer is:

$\cot O=(1)/((-3)/(8))$ or
$\cot 0=(-8)/(3)$

We know that the tangent trignometric function and the cotangent trignometric function is given by:

$\tan x=(1)/(\cot x)$

i.e. the tangent function and the cotangent function are inverse of each other.

We are given tangent of an angle O as:

$\tan 0=(-3)/(8)$

Hence, we have:

$\cot O=(1)/(\tan O)\\\\i.e.\\\\\cot O=(1)/((-3)/(8))\\\\i.e.\\\\\cot O=(8)/(-3)\\\\i.e.\\\\\cot 0=(-8)/(3)$