Math Problem Statement
Sur le cercle trigonométrique suivant, donner le réel dont le point A est l'image.
Solution
The question asks to determine the real value associated with the point on the given unit circle.
Solution:
From the diagram:
- The point is located in the first quadrant.
- The coordinates of are .
In the unit circle, the x-coordinate represents , and the y-coordinate represents . Therefore, we need to determine the angle such that:
This corresponds to the angle (or 30 degrees), since:
Final Answer:
The real number associated with the point is:
Let me know if you would like more detailed steps or additional help.
Related Questions:
- What is the process to calculate the angle for a different point on the unit circle?
- How are the sine and cosine functions defined on the unit circle?
- How does the unit circle relate to trigonometric identities?
- What are the coordinates of if rotated by radians?
- Can you determine the angle for ?
Tip:
Always ensure that you analyze whether the point is in the correct quadrant to verify the sign of sine and cosine.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Unit Circle
Angles and Radians
Formulas
cos(θ) = x-coordinate
sin(θ) = y-coordinate
Theorems
Definition of the Unit Circle
Suitable Grade Level
Grades 10-12