Does anyone understand this answer? proving sin(A-B)

  • Thread starter eeuler
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In summary, the conversation is about a person struggling to understand a trigonometric problem and asking for help from others. The key points mentioned include the person's difficulty grasping the first basic parts, having to look at the answer, and not understanding how to find the angle in the bottom right hand corner of the triangle. They also mention the possibility of a trigonometric identity being related to the problem. Another person chimes in and explains that the two non-right angles in a right triangle must add to pi/2 and clarifies the correct angle to be pi/2 - A. The first person expresses gratitude for the explanation.
  • #1
eeuler
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I had no clue how to do this and could only grasp the first basic parts but even then i couldn't get it right and in the end i had to look at the answer, which confused me even more. So i was wondering if anyone else understands this, and if so could you describe it in words please?

Homework Statement


6k4i3jt.jpg



Homework Equations


As above


The Attempt at a Solution


89jcqhs.jpg


I understand the first part, getting cos B from the graph...yet when it gets to the other part '...angle in the bottom right hand corner of the triangle is PI - A...' i don't understand how they came to that...but i was wondering, the sin (PI/2 - A) seems to be related to a trigonometric identity? If someone could explain it that would be great.
 
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  • #2
eeuler said:
I had no clue how to do this and could only grasp the first basic parts but even then i couldn't get it right and in the end i had to look at the answer, which confused me even more. So i was wondering if anyone else understands this, and if so could you describe it in words please?

Homework Statement


6k4i3jt.jpg



Homework Equations


As above


The Attempt at a Solution


89jcqhs.jpg


I understand the first part, getting cos B from the graph...yet when it gets to the other part '...angle in the bottom right hand corner of the triangle is PI - A...' i don't understand how they came to that...but i was wondering, the sin (PI/2 - A) seems to be related to a trigonometric identity? If someone could explain it that would be great.
The angle in the bottom right hand corner is NOT [itex]\pi- A[/itex]. The two non-right angles in a right triangle must add to [itex]\pi/2[/itex]. Since the whole angle in the upper left is A, the angle in the bottom righthand corner is [itex]\pi/2- A[/itex].
 
  • #3
Thank you for that, it clears some of the confusion, thanks.
 

FAQ: Does anyone understand this answer? proving sin(A-B)

What is the meaning of "sin(A-B)"?

The expression "sin(A-B)" refers to the sine of the difference between two angles, A and B. It is a trigonometric function that calculates the ratio of the side opposite the angle to the hypotenuse of a right triangle.

How is "sin(A-B)" related to proving an answer?

In mathematics, the expression "sin(A-B)" is often used in the process of proving an answer or solving a problem. It helps to simplify and manipulate equations involving trigonometric functions, making it easier to reach a solution.

What is the purpose of proving "sin(A-B)"?

The purpose of proving "sin(A-B)" is to validate the answer or solution to a problem. By using mathematical techniques, we can show that the result obtained is accurate and logical.

What are some common methods for proving "sin(A-B)"?

There are several methods for proving "sin(A-B)", including using trigonometric identities, using the unit circle, and using the properties of right triangles. Each method has its own advantages and is suitable for different types of problems.

Why is it important to understand "sin(A-B)" when solving mathematical problems?

Understanding "sin(A-B)" is crucial when solving mathematical problems because it is a fundamental trigonometric function that is used in various fields such as physics, engineering, and geometry. It allows us to solve complex problems involving triangles and angles, and is also essential in higher-level mathematics courses.

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