Unit circle

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/unit-circle

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the fundamental equation?Points (x,y) on the circumference satisfy x² + y² = 1
2. What is the trigonometric representation?Coordinates (x,y) correspond to (cos θ, sin θ) for angle θ
3. Why do we use the unit circle in math?It lets us define and understand sine, cosine, and tangent for all angles, not just right triangles. This is essential for trigonometry, calculus, and many scientific fields.
4. How do we find the sine and cosine of an angle using the unit circle?For an angle θ measured counterclockwise from the positive x‑axis, the point where the angle’s line meets the circle has coordinates (cos θ, sin θ). The cosine is the x‑coordinate and the sine is the y‑coordinate.

Cartesian Coordinate System: A system that uses perpendicular axes (x and y) to define the position of points in a plane.
Trigonometric Functions: Functions (like sine, cosine, tangent) that relate angles of a triangle to the lengths of its sides.
Pythagorean Theorem: A theorem stating that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.