2- According to the given values below, make necessary computations. a) Depending on the sign (that can be negative or positive) of the Ax and Ay, compute the angle a in grad unit. tan(a)= -0.725416 Tan(a)=-34546 (Ax negative) (Ay negative) b) Compute a angle values (in grad unit), which correspond to the trigonometric functions. sin(a)= 0.784567 cot(a)= 0.978244 c) Assume that a,B,y are the interior angles of a plane triangle. According to the given equations, compute the interior angles that do not given. α = 22° 15'37" B = 59° 45'24"+y
2- According to the given values below, make necessary computations. a) Depending on the sign (that can be negative or positive) of the Ax and Ay, compute the angle a in grad unit. tan(a)= -0.725416 Tan(a)=-34546 (Ax negative) (Ay negative) b) Compute a angle values (in grad unit), which correspond to the trigonometric functions. sin(a)= 0.784567 cot(a)= 0.978244 c) Assume that a,B,y are the interior angles of a plane triangle. According to the given equations, compute the interior angles that do not given. α = 22° 15'37" B = 59° 45'24"+y
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
![### Application of Trigonometry in Computing Angles
In this exercise, we will explore how trigonometric functions can be used to calculate angles based on given values. The steps will involve working with positive and negative signs of Δx and Δy, and computing angle values in grad units. We'll also calculate the interior angles of a plane triangle.
#### a) Compute the angle α in grad units given Δx and Δy
**When Δx (Δx negative):**
\[ \tan(\alpha) = -0.725416 \]
**When Δy (Δy negative):**
\[ \tan(\alpha) = -34546 \]
Depending on the given values of Δx and Δy, the sign (positive or negative) will affect the computation of the angle α in grad units.
#### b) Calculate α angle values in grad units
Given the trigonometric functions:
\[ \sin(\alpha) = 0.784567 \]
\[ \cot(\alpha) = 0.978244 \]
Using these values, you can compute the angle α in grad units.
#### c) Calculate the interior angles of a plane triangle
Assuming that α, β, and γ are the interior angles of a plane triangle, and using the provided equations:
\[ \alpha = 22^\circ 15' 37'' \]
\[ \beta = 59^\circ 45' 24'' + \gamma \]
To find the interior angles that are not given, you can use the fact that the sum of the interior angles of a triangle is always 180 degrees.
### Diagrams & Graphs Explanation
Currently, there are no diagrams or graphs associated with this problem set. However, for better understanding, one might consider visualizing a triangle with interior angles α, β, and γ. This can assist in visualizing how trigonometric functions apply to triangles and their angles.
### Conclusion
This exercise emphasizes the importance of understanding trigonometric functions and their applications in calculating angles. By working through these computations, students can grasp how trigonometry is used in various mathematical and real-world scenarios.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb34eb3b-53e5-4e6c-9638-9efc4a2e33af%2F07e242f9-f453-4a11-b487-8d43f8a2dad8%2F233267_processed.png&w=3840&q=75)
Transcribed Image Text:### Application of Trigonometry in Computing Angles
In this exercise, we will explore how trigonometric functions can be used to calculate angles based on given values. The steps will involve working with positive and negative signs of Δx and Δy, and computing angle values in grad units. We'll also calculate the interior angles of a plane triangle.
#### a) Compute the angle α in grad units given Δx and Δy
**When Δx (Δx negative):**
\[ \tan(\alpha) = -0.725416 \]
**When Δy (Δy negative):**
\[ \tan(\alpha) = -34546 \]
Depending on the given values of Δx and Δy, the sign (positive or negative) will affect the computation of the angle α in grad units.
#### b) Calculate α angle values in grad units
Given the trigonometric functions:
\[ \sin(\alpha) = 0.784567 \]
\[ \cot(\alpha) = 0.978244 \]
Using these values, you can compute the angle α in grad units.
#### c) Calculate the interior angles of a plane triangle
Assuming that α, β, and γ are the interior angles of a plane triangle, and using the provided equations:
\[ \alpha = 22^\circ 15' 37'' \]
\[ \beta = 59^\circ 45' 24'' + \gamma \]
To find the interior angles that are not given, you can use the fact that the sum of the interior angles of a triangle is always 180 degrees.
### Diagrams & Graphs Explanation
Currently, there are no diagrams or graphs associated with this problem set. However, for better understanding, one might consider visualizing a triangle with interior angles α, β, and γ. This can assist in visualizing how trigonometric functions apply to triangles and their angles.
### Conclusion
This exercise emphasizes the importance of understanding trigonometric functions and their applications in calculating angles. By working through these computations, students can grasp how trigonometry is used in various mathematical and real-world scenarios.
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