Solve Absolute Relative And Polar Coordinates
Introduction :
Introduction :
Absolute relative error is the measurement of the amount of physical error that are measured in the analysis of the period. Lets us say that the meter stick is used to calculate a given distance. The error is rather hastily made, but it is good to 1mm. This is called as the absolute error of the measurement. That is, Absolute error = 1mm (0.001m).The combination of angular co-ordinates and radial co-ordinates is said to be polar coordinates .Polar co-ordinates can written in the form of (r, 'theta' ) .
Example of Solve Absolute Relative Value:
Example 1:
Student calculates the mass of a sample to be 6.45 g. Actual mass of the sample is 8.42 g. find out the absolute error and relative error.
Solution:
Step 1: Experimental calculated Value = 6.45 g and Known Value = 8.42 g
Step 2: Absolute Error = Experimental calculated value - Known Value.
Step 3: Now we need to subtract 6.45 g - 8.42 g. Therefore absolute relative Error = - 1.97 g.
Step 4: Relative error = '"Error" /"unknown value"' .
Step 5: So, Relative Error = '(-1.97)/8.42' .
Step 6: Therefore, the relative error value is -0.233 g.
This is the example of solve absolute value.
Example Problem of Solve Polar Coordinates:
Example 2:
Explain the expression in an equation of a circle (x - a) ^2 + y^2 = a^2 in polar coordinates with its center at (a, 0) and radius a.
Solution:
Step 1: The given equation is (x - a)^ 2 + y^2 = a^2
Step 2: Expand the given equation. So, we get (x - a) 2 + y^2 = a^2
Step 3: It can be written as (x - a)^ 2 + y^2 = x2 - 2ax + a^2 + y^2 .
Step 4: Rearrange the obtained equation in simple form x2 + y^2 = 2ax
Step 5: Now we can use the equation Q2 = 2ax and x =Q cos in above equation.
Step 6: therefore Q^2 = 2aQ cos(Divide by Q both sides)
Step 7:Q = 2acos
This equation is the equation of the circle with its midpoint (a, 0) and radius an in polar coordinates.
This is the example of solve polar coordinates.
The radial coordinate is often denoted by r, and the angular coordinate by or t.
Angles in polar notation are generally expressed in either degrees or radians (2 rad being equal to 360). Degrees are traditionally used in navigation, surveying, and many applied disciplines, while radians are more common in mathematics and mathematical physics.[9]
In many contexts, a positive angular coordinate means that the angle is measured counterclockwise from the axis.
In mathematical literature, the polar axis is often drawn horizontal and pointing to the right.
Uniqueness of polar coordinates
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Adding any number of full turns (360) to the angular coordinate does not change the corresponding direction. Also, a negative radial coordinate is best interpreted as the corresponding positive distance measured in the opposite direction. Therefore, the same point can be expressed with an infinite number of different polar coordinates (r, n360) or (r, (2n + 1)180), where n is any integer.[10] Moreover, the pole itself can be expressed as (0, ) for any angle .[11]
Where a unique representation is needed for any point, it is usual to limit r to non-negative numbers (r 0) and to the interval [0, 360) or (180, 180] (in radians, [0, 2) or (, ]).[12] One must also choose a unique azimuth for the pole, e.g., = 0.
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