What is the Correct Method to Solve this Trigonometry Problem?

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SUMMARY

The correct method to solve the trigonometry problem involving sin a = –cos b = 3/5, where both angles are in the second quadrant, requires the application of the cosine subtraction formula. The user initially calculated cos(a - b) using arcsin and arccos functions but arrived at an incorrect answer of 0. The correct answer is 24/25, which emphasizes the importance of considering the multivalued nature of arcsin and arccos and identifying the appropriate solutions within the specified quadrant.

PREREQUISITES
  • Understanding of trigonometric identities and formulas, specifically the cosine subtraction formula.
  • Knowledge of the properties of the sine and cosine functions in different quadrants.
  • Familiarity with inverse trigonometric functions, particularly arcsin and arccos.
  • Ability to analyze multivalued functions and their implications in trigonometric contexts.
NEXT STEPS
  • Study the cosine subtraction formula in detail to understand its applications.
  • Learn about the properties of inverse trigonometric functions and their ranges in different quadrants.
  • Explore examples of solving trigonometric equations involving multiple angles.
  • Practice identifying the correct quadrant for trigonometric functions based on given conditions.
USEFUL FOR

Students revising trigonometry, educators teaching trigonometric identities, and anyone looking to deepen their understanding of angle relationships in trigonometric functions.

Gurdian
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Not homework just my own revision.

If sin a = –cos b = 3/5 and a and b are both in the second quadrant, what is cos (a – b)?

Now keep getting the answer 0, but the answer is apparently 24/25, now they use the trig subtraction formula, I just did cos ((arcsin(3/5) - arccos(-3/5)) I got 0 as the answer.

Was my method wrong, where did I go wrong with it?
 
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Both arcsin and arccos are multivalued. You need to get the possible solutions and see which are in the second quadrant.
 
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mathman said:
Both arcsin and arccos are multivalued. You need to get the possible solutions and see which are in the second quadrant.

Ah that's what the explanation was talking about.
 

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