Sin 2Q=20=2 sin a casa A 3 2.1.2√3/3 X=2√3 x=√√√3²-12 =√8=3√2 COD=
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°.
Related questions
Question
![### Trigonometric Identity and Triangle Calculation
To understand the trigonometric identity and the calculations shown, let's break down the steps to solve the given expressions and equations.
#### Trigonometric Identity
The identity used here is:
\[ \sin 2\theta = 2 \sin \theta \cos \theta \]
This identity is fundamental in trigonometry for transforming expressions involving double angles.
#### Diagram Breakdown
A right triangle is drawn with the following properties:
- The hypotenuse is labeled as 3.
- One of the legs (adjacent side) is 1.
- The other leg (opposite side) is calculated using the Pythagorean theorem.
#### Calculations
To find the unknown side \( x \):
\[ x = \sqrt{3^2 - 1^2} \]
\[ x = \sqrt{9 - 1} \]
\[ x = \sqrt{8} = 2\sqrt{2} \]
#### Cosine Calculation
The cosine of angle \(\theta\) is then calculated as:
\[ \cos \theta = \frac{2\sqrt{2}}{3} \]
#### Result Calculation
Using the above values:
\[ 2 \cdot \left(\frac{2\sqrt{2}}{3}\right) \]
The intermediate result becomes:
\[ = 4\frac{\sqrt{2}}{9} \]
The final boxed result:
\[ = -4 \frac{\sqrt{2}}{9} \]
#### Graph Explanation
If there were a graph in this image, explain the x-axis, y-axis, labels, trends, and any other relevant details to provide a comprehensive understanding.
**Note:** The red box around the final result indicates the solution to the given problem.
### Conclusion
This step-by-step breakdown helps comprehend the process followed to apply a trigonometric identity, use the Pythagorean theorem for calculating triangle sides, and simplifying trigonometric expressions. This topic is often covered in high school mathematics and is foundational for more advanced studies in trigonometry and calculus.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98691ce4-530e-4273-9fad-39e376c39b8c%2F4a1faee7-4b74-467a-9624-edeaa03d5a3c%2Fg3f7nyp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Trigonometric Identity and Triangle Calculation
To understand the trigonometric identity and the calculations shown, let's break down the steps to solve the given expressions and equations.
#### Trigonometric Identity
The identity used here is:
\[ \sin 2\theta = 2 \sin \theta \cos \theta \]
This identity is fundamental in trigonometry for transforming expressions involving double angles.
#### Diagram Breakdown
A right triangle is drawn with the following properties:
- The hypotenuse is labeled as 3.
- One of the legs (adjacent side) is 1.
- The other leg (opposite side) is calculated using the Pythagorean theorem.
#### Calculations
To find the unknown side \( x \):
\[ x = \sqrt{3^2 - 1^2} \]
\[ x = \sqrt{9 - 1} \]
\[ x = \sqrt{8} = 2\sqrt{2} \]
#### Cosine Calculation
The cosine of angle \(\theta\) is then calculated as:
\[ \cos \theta = \frac{2\sqrt{2}}{3} \]
#### Result Calculation
Using the above values:
\[ 2 \cdot \left(\frac{2\sqrt{2}}{3}\right) \]
The intermediate result becomes:
\[ = 4\frac{\sqrt{2}}{9} \]
The final boxed result:
\[ = -4 \frac{\sqrt{2}}{9} \]
#### Graph Explanation
If there were a graph in this image, explain the x-axis, y-axis, labels, trends, and any other relevant details to provide a comprehensive understanding.
**Note:** The red box around the final result indicates the solution to the given problem.
### Conclusion
This step-by-step breakdown helps comprehend the process followed to apply a trigonometric identity, use the Pythagorean theorem for calculating triangle sides, and simplifying trigonometric expressions. This topic is often covered in high school mathematics and is foundational for more advanced studies in trigonometry and calculus.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning