Evaluate the expression for A=90°, B=0°, and C=270°. sin A + 2 cos B g I sec B-3 csc C
Evaluate the expression for A=90°, B=0°, and C=270°. sin A + 2 cos B g I sec B-3 csc C
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
![### Problem Statement
Evaluate the expression for \( A = 90^\circ \), \( B = 0^\circ \), and \( C = 270^\circ \).
\[
\frac{\sin A + 2\cos B}{\sec B - 3\csc C}
\]
**Solution Steps:**
1. **Calculate Trigonometric Values:**
- \( \sin(90^\circ) = 1 \)
- \( \cos(0^\circ) = 1 \)
- \( \sec(0^\circ) = \frac{1}{\cos(0^\circ)} = 1 \)
- \( \csc(270^\circ) = \frac{1}{\sin(270^\circ)} = \frac{1}{-1} = -1 \)
2. **Substitute the Values:**
\[
\sin A + 2 \cos B = 1 + 2 \cdot 1 = 1 + 2 = 3
\]
\[
\sec B - 3\csc C = 1 - 3 \cdot (-1) = 1 + 3 = 4
\]
3. **Form the Expression:**
\[
\frac{\sin A + 2 \cos B}{\sec B - 3 \csc C} = \frac{3}{4}
\]
Thus, the evaluated expression yields a result of \( \frac{3}{4} \).
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**Continue Button:**
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**Note:** Always ensure proper substitutions and calculations when evaluating trigonometric expressions for specific angles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9ae2b74-0627-461f-a855-f05238f3c436%2F2991c188-b5f1-429f-9418-9ae49b8f0971%2Fe7elu73_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Evaluate the expression for \( A = 90^\circ \), \( B = 0^\circ \), and \( C = 270^\circ \).
\[
\frac{\sin A + 2\cos B}{\sec B - 3\csc C}
\]
**Solution Steps:**
1. **Calculate Trigonometric Values:**
- \( \sin(90^\circ) = 1 \)
- \( \cos(0^\circ) = 1 \)
- \( \sec(0^\circ) = \frac{1}{\cos(0^\circ)} = 1 \)
- \( \csc(270^\circ) = \frac{1}{\sin(270^\circ)} = \frac{1}{-1} = -1 \)
2. **Substitute the Values:**
\[
\sin A + 2 \cos B = 1 + 2 \cdot 1 = 1 + 2 = 3
\]
\[
\sec B - 3\csc C = 1 - 3 \cdot (-1) = 1 + 3 = 4
\]
3. **Form the Expression:**
\[
\frac{\sin A + 2 \cos B}{\sec B - 3 \csc C} = \frac{3}{4}
\]
Thus, the evaluated expression yields a result of \( \frac{3}{4} \).
**Graph/Diagram:**
There are no graphs or diagrams in the provided image. If there were any, detailed descriptions would be included here.
**Continue Button:**
There is a clickable "Continue" button at the bottom of the screen, which likely progresses the user to the next part of the lesson or evaluation.
**Note:** Always ensure proper substitutions and calculations when evaluating trigonometric expressions for specific angles.
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