cot 180°
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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![The image displays the text "cot 180°."
In trigonometry, "cot" stands for cotangent, which is the reciprocal of the tangent function. The cotangent of an angle is defined as the ratio of the adjacent side to the opposite side in a right-angled triangle. Mathematically:
\[ \cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta} \]
To understand this concept more deeply, let us evaluate the cotangent of 180°.
When dealing with trigonometric functions of specific angles, it's useful to consider the unit circle. The angle 180° corresponds to a point on the unit circle where the coordinates are (-1, 0).
For the angle 180°:
- \(\sin 180° = 0\)
- \(\cos 180° = -1\)
Using the definition of cotangent:
\[ \cot 180° = \frac{\cos 180°}{\sin 180°} = \frac{-1}{0} \]
Since division by zero is undefined, \(\cot 180°\) is undefined.
This fundamental understanding is crucial as it builds the foundational concepts for various trigonometric applications and identities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee38ad10-d3a7-46a8-a0c4-2e1f024f265a%2F7940b5b2-4fd2-42a5-980f-48600ab4d448%2F5ydu0ur_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays the text "cot 180°."
In trigonometry, "cot" stands for cotangent, which is the reciprocal of the tangent function. The cotangent of an angle is defined as the ratio of the adjacent side to the opposite side in a right-angled triangle. Mathematically:
\[ \cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta} \]
To understand this concept more deeply, let us evaluate the cotangent of 180°.
When dealing with trigonometric functions of specific angles, it's useful to consider the unit circle. The angle 180° corresponds to a point on the unit circle where the coordinates are (-1, 0).
For the angle 180°:
- \(\sin 180° = 0\)
- \(\cos 180° = -1\)
Using the definition of cotangent:
\[ \cot 180° = \frac{\cos 180°}{\sin 180°} = \frac{-1}{0} \]
Since division by zero is undefined, \(\cot 180°\) is undefined.
This fundamental understanding is crucial as it builds the foundational concepts for various trigonometric applications and identities.
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