Math Problem Statement
find exact value of cos 3𝜋 7 cos 2𝜋 21 + sin 3𝜋 7 sin 2𝜋 21
Solution
We can solve this expression using the cosine addition formula, which states:
In your case, the given expression is:
This matches the form of the cosine subtraction formula with and , so we can rewrite it as:
We need to subtract the angles inside the cosine:
Thus, the expression becomes:
The exact value of is:
Therefore, the exact value of is:
Would you like more details on this, or have any other questions?
Here are 5 related questions:
- How do you derive the cosine subtraction formula?
- What is the exact value of ?
- How can you apply the cosine formula to larger angles, like ?
- What is the sine subtraction formula, and when would you use it?
- Can you apply the cosine formula to angles in different quadrants?
Tip: Understanding how to manipulate angles in radians is key to simplifying trigonometric expressions effectively.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Angle subtraction formula
Cosine function
Formulas
Cosine addition formula
Cosine subtraction formula
Theorems
-
Suitable Grade Level
High School
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