If tant = 2, what is tan (t – 7)? Enter the exact answer. tan (t – 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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![### Trigonometry Problem
**Problem Statement:**
If \( \tan t = \frac{5}{7} \), what is \( \tan(t - \pi) \)?
Enter the exact answer in the space provided.
**Answer Input:**
\[ \tan(t - \pi) = \underline{\hspace{3cm}} \]
**Explanation:**
To solve for \( \tan(t - \pi) \), use the tangent subtraction formula. Knowing that \( \tan(t - \pi) \) equals to \( \tan(t) \), but with a change in sign based on the periodicity of the tangent function, you can determine the answer directly.
Given:
\[ \tan t = \frac{5}{7} \]
Since the tangent function has a period of \( \pi \):
\[ \tan(t - \pi) = \tan t \]
Therefore:
\[ \tan(t - \pi) = -\frac{5}{7} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b256bb6-7576-446c-ac07-c5d4136bf792%2F3762eb0f-7122-466d-ac7d-e6f4e44cb530%2Fpbs3ylj_processed.png&w=3840&q=75)
Transcribed Image Text:### Trigonometry Problem
**Problem Statement:**
If \( \tan t = \frac{5}{7} \), what is \( \tan(t - \pi) \)?
Enter the exact answer in the space provided.
**Answer Input:**
\[ \tan(t - \pi) = \underline{\hspace{3cm}} \]
**Explanation:**
To solve for \( \tan(t - \pi) \), use the tangent subtraction formula. Knowing that \( \tan(t - \pi) \) equals to \( \tan(t) \), but with a change in sign based on the periodicity of the tangent function, you can determine the answer directly.
Given:
\[ \tan t = \frac{5}{7} \]
Since the tangent function has a period of \( \pi \):
\[ \tan(t - \pi) = \tan t \]
Therefore:
\[ \tan(t - \pi) = -\frac{5}{7} \]
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