Math Problem Statement
The point P is on the unit circle. If the x-coordinate of P is 2/7, and P is in quadrant IV , then y = ?
Solution
To solve for the -coordinate of the point on the unit circle, we use the equation of the unit circle:
Given that the -coordinate of is and lies in quadrant IV (where the -coordinate is negative), we can substitute into the equation and solve for .
- Substitute into the equation:
- Simplify:
- Subtract from both sides:
- Take the square root of both sides:
Since is in quadrant IV, where the -coordinate is negative, we choose the negative root:
Thus, the -coordinate of point is .
Would you like more details or have any questions about this solution?
Here are 5 related questions:
- What is the equation of the unit circle in Cartesian coordinates?
- How do the signs of and vary in each quadrant?
- What is the significance of the unit circle in trigonometry?
- How do you find the coordinates of a point given its angle in the unit circle?
- Can you derive the distance formula from the equation of the unit circle?
Tip: Remember that in quadrant IV, the -coordinate is positive, and the -coordinate is negative.
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Math Problem Analysis
Mathematical Concepts
Unit Circle
Trigonometry
Coordinate Geometry
Formulas
x^2 + y^2 = 1
Theorems
Unit Circle Theorem
Suitable Grade Level
Grades 9-11