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Suppose, for some angle 0, cos(0) > O and cot(0) > 0. If the angle is drawn in standard position, what quadrant is it in? II O II O IV

Suppose, for some angle 0, cos(0) > O and cot(0) > 0. If the angle is drawn in standard position, what quadrant is it in? II O II O IV

Trigonometry (11th Edition)
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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**Trigonometric Quadrants and Angle Identification** **Question:** Suppose, for some angle θ, cos(θ) > 0 and cot(θ) > 0. If the angle is drawn in standard position, what quadrant is it in? **Options:** - I - II - III - IV **Explanation:** To determine in which quadrant the given angle θ lies where cos(θ) > 0 and cot(θ) > 0, we need to examine the properties of trigonometric functions in each quadrant: 1. **First Quadrant (Quadrant I):** - cos(θ) > 0 - cot(θ) > 0 (since both sine and cosine are positive, making their quotient positive) 2. **Second Quadrant (Quadrant II):** - cos(θ) < 0 - cot(θ) < 0 (since cosine is negative and sine is positive, making their quotient negative) 3. **Third Quadrant (Quadrant III):** - cos(θ) < 0 - cot(θ) > 0 (since both sine and cosine are negative, making their quotient positive) 4. **Fourth Quadrant (Quadrant IV):** - cos(θ) > 0 - cot(θ) < 0 (since cosine is positive and sine is negative, making their quotient negative) Given the conditions cos(θ) > 0 and cot(θ) > 0, we can conclude that θ is in the First Quadrant (Quadrant I).
Transcribed Image Text:**Trigonometric Quadrants and Angle Identification** **Question:** Suppose, for some angle θ, cos(θ) > 0 and cot(θ) > 0. If the angle is drawn in standard position, what quadrant is it in? **Options:** - I - II - III - IV **Explanation:** To determine in which quadrant the given angle θ lies where cos(θ) > 0 and cot(θ) > 0, we need to examine the properties of trigonometric functions in each quadrant: 1. **First Quadrant (Quadrant I):** - cos(θ) > 0 - cot(θ) > 0 (since both sine and cosine are positive, making their quotient positive) 2. **Second Quadrant (Quadrant II):** - cos(θ) < 0 - cot(θ) < 0 (since cosine is negative and sine is positive, making their quotient negative) 3. **Third Quadrant (Quadrant III):** - cos(θ) < 0 - cot(θ) > 0 (since both sine and cosine are negative, making their quotient positive) 4. **Fourth Quadrant (Quadrant IV):** - cos(θ) > 0 - cot(θ) < 0 (since cosine is positive and sine is negative, making their quotient negative) Given the conditions cos(θ) > 0 and cot(θ) > 0, we can conclude that θ is in the First Quadrant (Quadrant I).
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