Math Problem Statement
Compute tan(pi/12)
Solution
The exact value of can be calculated using the identity:
We can express this as the difference of angles formula for tangent:
Using the tangent subtraction formula:
Substituting and :
We know:
Now substitute these values:
Simplify the expression:
This simplifies to:
Thus, the exact value of is:
Would you like further clarification on this calculation?
Here are 5 related questions:
- How can the tangent addition formula be used for other angle combinations?
- What is the relationship between radians and degrees in trigonometry?
- How can you find the exact values of sine and cosine for common angles?
- What are some methods for simplifying trigonometric expressions involving square roots?
- How can trigonometric identities be applied to solve real-world problems?
Tip: Memorizing key angle values in both degrees and radians simplifies working with trigonometric identities.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Trigonometry
Angle Identities
Formulas
tan(A - B) = (tan(A) - tan(B)) / (1 + tan(A) * tan(B))
tan(45°) = 1
tan(30°) = 1 / sqrt(3)
Theorems
Tangent Subtraction Formula
Suitable Grade Level
Grades 10-12
Related Recommendation
Simplifying tan(π/12) Using the Tangent Difference Formula
Calculate tan(-π/12) Using Angle Addition Formula
Find the Exact Value of tan(17π/12) Using the Angle Addition Formula
Find the Exact Value of tan(π/12) Using Sum and Difference Identities
How to Calculate tan(11π/12) Using Trigonometric Identities