Math Problem Statement
how is 4cos(pi/6) equal 2sqrt3 shouldnt it be 4/2 since cos(pi/6) = 1/2 then multiple by 4 ?
Solution
Let's clarify this step-by-step to make sure we are on the same page:
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You are working with the expression .
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Step 1: Find .
- From trigonometric values, we know that .
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Step 2: Multiply the result by 4:
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Step 3: Simplify the expression:
So the expression simplifies to .
Your confusion:
- You mentioned that you thought , but actually .
- When you multiply by 4, you get , not , hence the result is .
Would you like more details or have any questions on this? Here are some follow-up questions that might help deepen your understanding:
- Why does ?
- How can we visualize on the unit circle?
- What are some other trigonometric values of common angles (like or )?
- How does simplifying trigonometric expressions help in solving problems efficiently?
- What are the differences between the sine and cosine functions in terms of the unit circle?
Tip: Always double-check the values of standard trigonometric functions for common angles like , , and so you can solve expressions quickly!
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Cosine Function
Formulas
cos(π/6) = √3/2
4 * cos(π/6)
Theorems
Basic Trigonometric Identities
Suitable Grade Level
Grades 9-11