📚 Topic Summary
Trigonometric functions on the coordinate plane extend the basic trig ratios (sine, cosine, tangent, etc.) beyond acute angles. Instead of a right triangle, we use a point (x, y) on the coordinate plane and its distance from the origin, denoted as 'r'. This allows us to define trig functions for any angle, positive or negative. The relationships are as follows: $\sin(\theta) = \frac{y}{r}$, $\cos(\theta) = \frac{x}{r}$, and $\tan(\theta) = \frac{y}{x}$. The value of 'r' is found using the Pythagorean theorem: $r = \sqrt{x^2 + y^2}$. Mastering these relationships is key to understanding trigonometry in Algebra 2.
This quiz will test your knowledge of trigonometric functions on the coordinate plane. Good luck!
🧮 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Sine |
A. The distance from the origin to the point (x, y). |
| 2. Cosine |
B. The ratio of the y-coordinate to r. |
| 3. Tangent |
C. The ratio of the x-coordinate to r. |
| 4. Radius (r) |
D. The ratio of the y-coordinate to the x-coordinate. |
| 5. Coordinate Plane |
E. A two-dimensional surface formed by the intersection of a horizontal number line (x-axis) and a vertical number line (y-axis). |
Match the numbers (1-5) with the correct letters (A-E).
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided below.
When working with trigonometric functions on the coordinate plane, we use the coordinates of a ________, (x, y), and the ________, 'r', which is the distance from the origin to that point. The sine of an angle, $\theta$, is defined as the ratio of the ________ to 'r'. The cosine of $\theta$ is the ratio of the ________ to 'r', and the tangent of $\theta$ is the ratio of the y-coordinate to the ________. To find 'r', we use the ________ theorem: $r = \sqrt{x^2 + y^2}$.
Word Bank: x-coordinate, Pythagorean, point, radius, y-coordinate
🤔 Part C: Critical Thinking
Explain how the signs (+ or -) of x and y in different quadrants of the coordinate plane affect the signs of the trigonometric functions (sine, cosine, and tangent). Provide specific examples.
