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Normal form
x cos α + y sin α = p
Where: α = Normal form, p = p, x = x, y = y
Solved example
Given: p = 7, x = 5, y = 10
Find: alpha (Normal form)
- Formula: x·cos(α) + y·sin(α) = p
- Rearranged for α: α = 2·atan((y - √(-p² + x² + y²))/(p + x))
- Substitute the values: α = 2·atan((10 - √(10² + 5² - 7²))/(5 + 7))
- Rearranged for α: α = 2·atan((y + √(-p² + x² + y²))/(p + x))
- Substitute the values: α = 2·atan((10 + √(10² + 5² - 7²))/(5 + 7))
- Result: α = 0.212893 rad = 12.197848° ; α = 2.001405 rad = 114.67205°
Answer: alpha = 0.212893 rad = 12.197848°
Calculator
How to calculate Normal form
- Write down the formula: x cos α + y sin α = p.
- Note the known values (p, x, y).
- Substitute them and simplify to find alpha.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Normal form?
The formula is x cos α + y sin α = p, where α = Normal form, p = p, x = x, y = y.
What is Normal form when p = 7, x = 5, y = 10?
alpha = 0.212893 rad = 12.197848°. Substitute the values into x cos α + y sin α = p and simplify.