Use a Sum-to-Product Formula to show the following. sin(140°) – sin(100°) = -sin(20°) Use a Sum-to-Product Formula for Sine and simplify. sin(140°) – sin(100°) = 2 cos sin 2 sin cos sin(20°) Need Help? Read It Watch It
Use a Sum-to-Product Formula to show the following. sin(140°) – sin(100°) = -sin(20°) Use a Sum-to-Product Formula for Sine and simplify. sin(140°) – sin(100°) = 2 cos sin 2 sin cos sin(20°) Need Help? Read It Watch It
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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Question
Could you please write the questions clearly and understandably? Thank you.
![**Title: Using Sum-to-Product Formulas**
**Objective:**
Learn how to use the Sum-to-Product Formula to show that:
\[ \sin(140^\circ) - \sin(100^\circ) = -\sin(20^\circ) \]
**Instructions:**
1. **Apply the Sum-to-Product Formula:**
\[
\sin(140^\circ) - \sin(100^\circ) = 2 \cos \left( \frac{\_}{2} \right) \sin \left( \frac{\_}{2} \right)
\]
2. **Calculate specific terms:**
- \[
= 2 \cos \left( \frac{240^\circ}{2} \right) \sin \left( \frac{40^\circ}{2} \right)
\]
- \[
= 2 \cos(120^\circ) \sin(20^\circ)
\]
3. **Continue Simplification:**
- \[
= \_\_ \sin(20^\circ)
\]
4. **Final Answer:**
- \[
= -\sin(20^\circ)
\]
**Support:**
- **Need Help?** Click on "Read It" or "Watch It" for additional guidance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3bcaea97-3c57-4685-8473-33f5b83e373d%2F8ca7b2be-e360-43bb-bb08-96141faf683e%2F4f4hhan_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Using Sum-to-Product Formulas**
**Objective:**
Learn how to use the Sum-to-Product Formula to show that:
\[ \sin(140^\circ) - \sin(100^\circ) = -\sin(20^\circ) \]
**Instructions:**
1. **Apply the Sum-to-Product Formula:**
\[
\sin(140^\circ) - \sin(100^\circ) = 2 \cos \left( \frac{\_}{2} \right) \sin \left( \frac{\_}{2} \right)
\]
2. **Calculate specific terms:**
- \[
= 2 \cos \left( \frac{240^\circ}{2} \right) \sin \left( \frac{40^\circ}{2} \right)
\]
- \[
= 2 \cos(120^\circ) \sin(20^\circ)
\]
3. **Continue Simplification:**
- \[
= \_\_ \sin(20^\circ)
\]
4. **Final Answer:**
- \[
= -\sin(20^\circ)
\]
**Support:**
- **Need Help?** Click on "Read It" or "Watch It" for additional guidance.
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