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# 1. Is the cotangent function odd, even, or neither odd nor even?

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1. Is the cotangent function odd, even, or neither odd nor even?

The cotangent function is   ________.

i think its odd?

Mar 4, 2020

#1
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If it is odd then it has 180 degree rotational symmetry around the origin.

This means that   Cot(theta) = -Cot(-theta)

If this is true then it is odd.

If theta is acute then it is in the 1st quad and   -theta is in the 4th quad

The absolute value of cot(theta) and cot(-theta) will be the same.

Tan is pos  in the 1st quadrant  and negative in 4th quadrant

so Cot is pos in positive in 1st and negative in 4th quadrant

therefore the statement is true

Cot is an odd function.

Mar 4, 2020

#1
+112024
+2

If it is odd then it has 180 degree rotational symmetry around the origin.

This means that   Cot(theta) = -Cot(-theta)

If this is true then it is odd.

If theta is acute then it is in the 1st quad and   -theta is in the 4th quad

The absolute value of cot(theta) and cot(-theta) will be the same.

Tan is pos  in the 1st quadrant  and negative in 4th quadrant

so Cot is pos in positive in 1st and negative in 4th quadrant

therefore the statement is true

Cot is an odd function.

Melody Mar 4, 2020
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thank you so much for going in depth with your response it really helps! im glad i got my answer confrimed with you and that i was correct! thanks for the information, i will keep it in mind

jjennylove  Mar 4, 2020
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You are very welcome Jenny.

Melody  Mar 4, 2020
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Very nice  explanation, Melody   !!!!

[ This sometimes  confuses  me  on these trig functions, too  !!!!   ]

CPhill  Mar 4, 2020
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Thanks Chris :)

Melody  Mar 4, 2020
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A general comment:

Jenny it is worth putting in effort to understanding the relevance of the unit circle (in relation to trig)

I remember lacking all understanding of the relevance of it when I was at school but when I worked it out later on it was like a light turned on for me.

This comment is not specifically relevant to this question it's just a general comment.

Mar 4, 2020
#7
+1998
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It helps to know comments like that,  I will definitely ,definitely.... keep note of that and contuine practicing to make sure I fully understand. Thanks for the input

jjennylove  Mar 4, 2020