Math Problem Statement
Convert the Polar coordinate to its Rectangular components.
Given Angle = 312° 43’ 15” and Distance = 16.82
Solution
To convert the given polar coordinates (angle and distance) to rectangular components, we'll use the following formulas:
Where:
- is the distance (16.82 units)
- is the angle (312° 43' 15")
We first need to convert the angle from degrees, minutes, and seconds into decimal degrees:
Then we will substitute the decimal value of and the distance into the rectangular coordinate formulas.
Let me compute the values.The angle in decimal degrees is approximately 312.72°.
Using the polar coordinates (distance = 16.82, angle = 312° 43' 15"), the rectangular components are:
Let me know if you'd like more details or have any questions! Here are some related questions:
- How would the results change if the angle were in radians instead of degrees?
- What is the general procedure for converting rectangular coordinates back to polar form?
- How does the cosine and sine function relate to the directional components in navigation (e.g., North-East)?
- Can the distance ever be negative in polar coordinates, and how would that affect the result?
- What would the rectangular components be if the angle were 45° instead of 312°?
Tip: Always remember to convert degrees to radians when using trigonometric functions in most programming languages!
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Polar and Rectangular Coordinates
Unit Conversion
Formulas
x = r * cos(θ)
y = r * sin(θ)
θ (decimal) = Degrees + (Minutes / 60) + (Seconds / 3600)
Theorems
Pythagorean theorem (for conversion between polar and rectangular coordinates)
Trigonometric functions (cosine and sine)
Suitable Grade Level
Grades 10-12
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