How Do You Calculate cos(a-b) from Given Sine and Cosine Values?

  • Thread starter Michael_Light
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    Trigonometry
In summary, we are given the equations sin(a) + cos(b) = 31/2/2 and sin(a) + sin(b) = 3/2 and asked to find cos(a-b). By using the Pythagorean identity and rewriting it in terms of sin(a), we can find two solutions for cos(a-b): 0.2599 and 0.7858. The given answer of 0.5 does not match either solution, suggesting a possible typo in the problem or answer.
  • #1
Michael_Light
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Homework Statement



Given that
sin(a) + cos(b) = 31/2/2 and
sin(a) + sin(b) = 3/2

Find cos(a-b)

Homework Equations





The Attempt at a Solution



Can anyone give me some hints?
 
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  • #2
See: http://file.glpacademy.co.kr/eTAP/mathfiles/english/trigo/lesson2/instructiontutor_last.html

ehild
 
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  • #3
Try taking the Pythagorean identity
cos2 b + sin2 b = 1

and rewriting it in terms of sin a. I found an answer by starting this way, but it is a decimal approximation.
 
  • #4
The answer i get is 0.7858... but the answer given is 0.5. What answer do you guys get?
 
Last edited:
  • #5
0.7858... is what I got, too. Maybe there is a typo in the original problem or in the answer?
 
  • #6
I get a total of 2 solutions: 0.2599 and 0.7858
 

Related to How Do You Calculate cos(a-b) from Given Sine and Cosine Values?

1. What is trigonometry?

Trigonometry is a branch of mathematics that focuses on the relationships and calculations involving angles and triangles. It is used to solve problems related to measurements of sides and angles of triangles.

2. What is the cosine function?

The cosine function (cos) is one of the primary trigonometric functions. It is used to calculate the ratio of the adjacent side to the hypotenuse in a right triangle. In other words, it represents the relationship between the length of the adjacent side and the length of the hypotenuse.

3. How do you find cos(a-b)?

To find cos(a-b), you can use the trigonometric identity: cos(a-b) = cos(a)cos(b) + sin(a)sin(b). This means that you can multiply the cosines of the two angles and add the products of the sines of the two angles.

4. What is the difference between cos(a-b) and cos(a) - cos(b)?

There is a difference in the calculation and meaning of these two expressions. Cos(a-b) is the cosine of the difference between two angles, while cos(a) - cos(b) is the difference between the cosines of two angles. It is important to understand the context in which these expressions are used to avoid confusion.

5. How is trigonometry used in real life?

Trigonometry has many real-life applications, such as in architecture, engineering, navigation, and astronomy. It is used to calculate distances and heights, determine angles and directions, and solve problems related to waves and oscillations. It is also used in computer graphics and game development.

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