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

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    Trigonometry
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Homework Help Overview

The problem involves calculating cos(a-b) using given values for sin(a) and cos(b), along with a second equation involving sin(b). The context is trigonometry.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss using the Pythagorean identity to relate the sine and cosine values. There are attempts to rewrite the equations in terms of sin(a) and explore potential discrepancies in the provided answers.

Discussion Status

Multiple participants have shared their calculated values for cos(a-b), noting discrepancies with the expected answer. There is an ongoing exploration of possible typos in the problem statement or the provided answer.

Contextual Notes

Participants are working with specific values and equations, but there is uncertainty regarding the accuracy of the original problem or the expected results.

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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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See: http://file.glpacademy.co.kr/eTAP/mathfiles/english/trigo/lesson2/instructiontutor_last.html

ehild
 
Last edited by a moderator:
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.
 
The answer i get is 0.7858... but the answer given is 0.5. What answer do you guys get?
 
Last edited:
0.7858... is what I got, too. Maybe there is a typo in the original problem or in the answer?
 
I get a total of 2 solutions: 0.2599 and 0.7858
 

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