Equivalent Expression for cot(-π/4) in Terms of Acute Angle

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Homework Help Overview

The discussion revolves around finding an equivalent expression for cot(-π/4) in terms of an acute angle. Participants are exploring the properties of cotangent and the definitions of acute and reflex angles within the context of trigonometric functions.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the interpretation of negative angles on the unit circle and the resulting quadrant placement. There is confusion regarding whether -π/4 can be classified as acute and the implications of this classification on the equivalent expression.

Discussion Status

Multiple interpretations are being explored, particularly regarding the classification of angles and the correct equivalent expression. Some participants express agreement on the classification of 3π/4 as a reflex angle, while others affirm the correctness of π/4 as an acute angle. The discussion remains open without a definitive consensus.

Contextual Notes

Participants note that the definition of acute angles typically applies to positive angles and express uncertainty about how this applies to negative angles like -π/4. There is also mention of textbook discrepancies regarding the expected answers.

Veronica_Oles
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Homework Statement


State an equivalent expression in terms of the related acute angle?
(A) cot(-π/4)

Homework Equations

The Attempt at a Solution


(A) I made the the unit circle and since its negative I went clockwise and made it into the fourth quadrant. I ended up getting -cotπ/4. However the answer is not the one that the textbook has given. I am a little confused.
The textbook has given the answer cot3π/4, but I thought we were supposed to go clockwise because it is negative?
 
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Veronica_Oles said:

Homework Statement


State an equivalent expression in terms of the related acute angle?
(A) cot(-π/4)

Homework Equations

The Attempt at a Solution


(A) I made the the unit circle and since its negative I went clockwise and made it into the fourth quadrant. I ended up getting -cotπ/4. However the answer is not the one that the textbook has given. I am a little confused.
The textbook has given the answer cot3π/4, but I thought we were supposed to go clockwise because it is negative?

An acute angle is one that is less than ##\pi /2##. I've never seen this used for negative angles, so I'm not sure whether ##-\pi /4## would be considered acute. In any case, ##3\pi /4## is not an acute angle. It's actually a "reflex" angle (I had to look that one up).

I thought your answer was correct. ##\pi /4## is definitely an acute angle.
 
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I agree with @PeroK -- ##3\pi/4## is not an acute angle.
PeroK said:
It's actually a "relflex" angle (I had to look that one up).
I'll bet what you actually looked up was "reflex". :oldbiggrin:
 
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PeroK said:
An acute angle is one that is less than ##\pi /2##. I've never seen this used for negative angles, so I'm not sure whether ##-\pi /4## would be considered acute. In any case, ##3\pi /4## is not an acute angle. It's actually a "reflex" angle (I had to look that one up).

I thought your answer was correct. ##\pi /4## is definitely an acute angle.
I just asked my teacher, I got the angle correct. Thx.
 

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