The point P(x.y) on the unit circle that corresponds to a real number t is given. Find the values of the indicated trigonometric function at t. 6. Find cot t. 9. V77 OA. 9. 6. O B. V77 C. O D. 92 2/9
The point P(x.y) on the unit circle that corresponds to a real number t is given. Find the values of the indicated trigonometric function at t. 6. Find cot t. 9. V77 OA. 9. 6. O B. V77 C. O D. 92 2/9
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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![**Trigonometry Problem: Finding Cotangent on the Unit Circle**
---
**Problem Statement:**
The point \(P(x, y)\) on the unit circle corresponds to a real number \(t\). Find the values of the indicated trigonometric function at \(t\):
\[
\left( -\frac{\sqrt{77}}{9}, \frac{2}{9} \right)
\]
Find \(\cot t\).
**Options:**
- **A.** \(\frac{\sqrt{77}}{9}\)
- **B.** \(-\frac{9}{2}\)
- **C.** -\(\frac{\sqrt{77}}{2}\)
- **D.** \(\frac{2}{9}\)
---
To solve this problem, remember that the cotangent function is defined as the ratio of the cosine to the sine of an angle in a right triangle or on the unit circle:
\[
\cot t = \frac{\cos t}{\sin t}
\]
Given the coordinates (-\(\sqrt{77}/9\), 2/9), we can substitute these values into the formula:
\[
\cot t = \frac{\cos t}{\sin t} = \frac{-\sqrt{77}/9}{2/9} = -\frac{\sqrt{77}}{2}
\]
Therefore, the correct answer is:
**Option C: -\(\frac{\sqrt{77}}{2}\)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad727bdc-baba-4947-a2e3-e934fc451c32%2F7f461db8-288b-43aa-b4b9-dc684edc0f10%2Fmhdl3bb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Trigonometry Problem: Finding Cotangent on the Unit Circle**
---
**Problem Statement:**
The point \(P(x, y)\) on the unit circle corresponds to a real number \(t\). Find the values of the indicated trigonometric function at \(t\):
\[
\left( -\frac{\sqrt{77}}{9}, \frac{2}{9} \right)
\]
Find \(\cot t\).
**Options:**
- **A.** \(\frac{\sqrt{77}}{9}\)
- **B.** \(-\frac{9}{2}\)
- **C.** -\(\frac{\sqrt{77}}{2}\)
- **D.** \(\frac{2}{9}\)
---
To solve this problem, remember that the cotangent function is defined as the ratio of the cosine to the sine of an angle in a right triangle or on the unit circle:
\[
\cot t = \frac{\cos t}{\sin t}
\]
Given the coordinates (-\(\sqrt{77}/9\), 2/9), we can substitute these values into the formula:
\[
\cot t = \frac{\cos t}{\sin t} = \frac{-\sqrt{77}/9}{2/9} = -\frac{\sqrt{77}}{2}
\]
Therefore, the correct answer is:
**Option C: -\(\frac{\sqrt{77}}{2}\)**
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