Trigonometry Signs by Quadrant Practice Sheet (PDF)

📚 Topic Summary

Understanding the signs of trigonometric functions in different quadrants is crucial for solving trigonometry problems. The coordinate plane is divided into four quadrants, and in each quadrant, the trigonometric functions (sine, cosine, tangent, etc.) have specific signs (+ or -). Remembering which functions are positive in which quadrants can be simplified using mnemonics like "All Students Take Calculus" or "CAST". This worksheet will guide you through practicing these sign conventions.

A quadrant is one of the four regions into which the coordinate plane is divided by the x-axis and y-axis. Understanding the $(x, y)$ coordinate signs in each quadrant is essential for determining the signs of trigonometric functions. For example, in Quadrant I, both $x$ and $y$ are positive, so sine, cosine, and tangent are all positive. In Quadrant II, $x$ is negative and $y$ is positive, so only sine is positive.

🔤 Part A: Vocabulary

Match the term with its correct definition:

1. Term: Quadrant
2. Term: Sine
3. Term: Cosine
4. Term: Tangent
5. Term: Unit Circle

1. Definition: The ratio of the opposite side to the hypotenuse in a right triangle.
2. Definition: A circle with a radius of 1, centered at the origin.
3. Definition: One of the four regions of the coordinate plane.
4. Definition: The ratio of the adjacent side to the hypotenuse in a right triangle.
5. Definition: The ratio of the sine to the cosine.

✍️ Part B: Fill in the Blanks

Complete the following paragraph with the correct words:

In Quadrant ____, both sine and cosine are positive. In Quadrant II, only ______ is positive. In Quadrant III, only _______ is positive. Finally, in Quadrant IV, only _______ is positive. The mnemonic _______ can help you remember these rules.

🤔 Part C: Critical Thinking

Explain why knowing the signs of trigonometric functions in each quadrant is important for solving trigonometric equations and finding angles.