If tan 55° = 10/7, which is true? tan 35⁰ = 7/10 O cos 35º = 7/10 O tan 55⁰ = 7/10 Otan 35º = 10/7
If tan 55° = 10/7, which is true? tan 35⁰ = 7/10 O cos 35º = 7/10 O tan 55⁰ = 7/10 Otan 35º = 10/7
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Title: Trigonometry Problem - True Statement Identification
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**Problem:**
Given that \( \tan 55^\circ = \frac{10}{7} \), determine which of the following statements is true:
1. \( \tan 35^\circ = \frac{7}{10} \)
2. \( \cos 35^\circ = \frac{7}{10} \)
3. \( \tan 55^\circ = \frac{7}{10} \)
4. \( \tan 35^\circ = \frac{10}{7} \)
**Explanation:**
This problem requires an understanding of trigonometric identities and properties, such as the complementary angle relationships in trigonometric functions. Specifically, it tests knowledge of the tangent function for complementary angles, where:
\[ \tan(90^\circ - \theta) = \cot(\theta) \]
In this context, \( \tan 35^\circ = \cot 55^\circ = \frac{1}{\tan 55^\circ} = \frac{7}{10} \).
Thus, the correct statement is:
1. \( \tan 35^\circ = \frac{7}{10} \)
The solution above provides a direct application of these trigonometric principles to solve the problem accurately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8946c7ff-a7db-4ece-95ac-6256e20973be%2F6353b202-3dd3-48fc-827e-6e71f678f114%2Fs08ubti_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Title: Trigonometry Problem - True Statement Identification
---
**Problem:**
Given that \( \tan 55^\circ = \frac{10}{7} \), determine which of the following statements is true:
1. \( \tan 35^\circ = \frac{7}{10} \)
2. \( \cos 35^\circ = \frac{7}{10} \)
3. \( \tan 55^\circ = \frac{7}{10} \)
4. \( \tan 35^\circ = \frac{10}{7} \)
**Explanation:**
This problem requires an understanding of trigonometric identities and properties, such as the complementary angle relationships in trigonometric functions. Specifically, it tests knowledge of the tangent function for complementary angles, where:
\[ \tan(90^\circ - \theta) = \cot(\theta) \]
In this context, \( \tan 35^\circ = \cot 55^\circ = \frac{1}{\tan 55^\circ} = \frac{7}{10} \).
Thus, the correct statement is:
1. \( \tan 35^\circ = \frac{7}{10} \)
The solution above provides a direct application of these trigonometric principles to solve the problem accurately.
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