Math Problem Statement
Find the exact value of cos(5π/12).
Solution
The problem asks for the exact value of .
To solve this, let's break down into angles whose cosine values we know. We can use the sum or difference identities for cosine to find the exact value.
Step-by-Step Solution
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Rewrite as a sum:
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Use the Cosine Sum Identity:
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Substitute Values:
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Calculate:
Final Answer
The exact value is:
Would you like further details on how to apply trigonometric identities, or do you have other questions?
Additional Practice Questions:
- What is the exact value of ?
- How can you use the sine sum identity to find ?
- What is using sum identities?
- How do you simplify ?
- Find the exact value of .
Tip: Always look for ways to rewrite angles in terms of known values, as this often simplifies complex trigonometric calculations.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Trigonometric Identities
Cosine Sum Identity
Formulas
Cosine sum identity: cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
Theorems
Cosine Sum Identity
Suitable Grade Level
Grade 11-12