- #1
Did I Make a Mistake in my Coordinates? Help Needed!
- Context: Undergrad
- Thread starter Shafia Zahin
- Start date
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- Tags
- Confusion Coordinates
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SUMMARY
The discussion centers on the correct labeling of coordinates for point B in a Cartesian plane, specifically whether the coordinates should be (a cos θ, a sin θ) or (-a cos θ, a sin θ). It is established that the labeling is correct as (a cos θ, a sin θ) when considering the properties of cosine in the second and third quadrants, where cos θ is negative for angles between π/2 and 3π/2. The confusion arises from treating the x-coordinate as a length without considering its position relative to the origin, necessitating a negative sign for the x-coordinate in certain contexts.
PREREQUISITES- Understanding of Cartesian coordinates
- Knowledge of trigonometric functions, particularly cosine and sine
- Familiarity with the unit circle and angle quadrants
- Basic geometry concepts related to triangle construction
- Study the properties of trigonometric functions in different quadrants
- Learn about the unit circle and its application in coordinate systems
- Explore triangle construction techniques in geometry
- Investigate the implications of coordinate transformations in physics and engineering
Students and educators in mathematics, particularly those studying trigonometry and geometry, as well as anyone involved in physics or engineering requiring a solid understanding of coordinate systems and trigonometric functions.
- #2
Fightfish
- 953
- 118
No there is nothing wrong with the labeling of the coordinates in the diagram. Recall that ##\cos \theta## is negative for ##\pi/2 < \theta < 3\pi/2## (or what you may know as the second and third quadrants).
- #3
- #4
Fightfish
- 953
- 118
When you did the triangle construction in your diagram, you treated ##x## there as a length, which only takes on positive values, but ignored its position relative to where the origin was defined. So, the x-coordinate of the point should in fact be the negative of the ##x## in your derivation.
- #5
Shafia Zahin
- 31
- 1
Oh,now I got it,thank you so muchFightfish said:
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