Prove the identity. sin(x - 1) = sin(x) Use the Subtraction Formula for Sine, and then simplify. sin(x - π) = (sin(x))( = (sin(x))( 11 1)-(cos(x) (sin(7)) |)-(cos(x))(0)

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°.
Question
### Prove the Identity

**Identity:**
\[ \sin(x - \pi) = -\sin(x) \]

**Instructions:**
Use the Subtraction Formula for Sine, and then simplify.

**Step-by-Step Solution:**

1. **Apply the Subtraction Formula for Sine:**
\[ \sin(x - \pi) = \sin(x)\cos(\pi) - \cos(x)\sin(\pi) \]

2. **Substitute the known values:**
   \[ \cos(\pi) = -1 \]
   \[ \sin(\pi) = 0 \]

Thus, the expression becomes:
\[ \sin(x - \pi) = \sin(x)(-1) - \cos(x)(0) \]

3. **Simplify the expression:**
\[ \sin(x - \pi) = -\sin(x) \]

**Conclusion:**
The original identity \(\sin(x - \pi) = -\sin(x)\) is proved through the Subtraction Formula for Sine.
Transcribed Image Text:### Prove the Identity **Identity:** \[ \sin(x - \pi) = -\sin(x) \] **Instructions:** Use the Subtraction Formula for Sine, and then simplify. **Step-by-Step Solution:** 1. **Apply the Subtraction Formula for Sine:** \[ \sin(x - \pi) = \sin(x)\cos(\pi) - \cos(x)\sin(\pi) \] 2. **Substitute the known values:** \[ \cos(\pi) = -1 \] \[ \sin(\pi) = 0 \] Thus, the expression becomes: \[ \sin(x - \pi) = \sin(x)(-1) - \cos(x)(0) \] 3. **Simplify the expression:** \[ \sin(x - \pi) = -\sin(x) \] **Conclusion:** The original identity \(\sin(x - \pi) = -\sin(x)\) is proved through the Subtraction Formula for Sine.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

im confused on the way you solved the probelm can you write out the answer because it is not clear!

Solution
Bartleby Expert
SEE SOLUTION
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry
Algebra and Trigonometry
Trigonometry
ISBN:
9781938168376
Author:
Jay Abramson
Publisher:
OpenStax
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning