Signs of Trigonometric Functions
Drag the point on the circle or use the slider to see the signs change.
A Quick Guide to the Quadrants
Quadrant I (0° to 90°)
All functions are positive. Both x (cosine) and y (sine) coordinates are positive.
Quadrant II (90° to 180°)
Sine is positive. The x-coordinate (cosine) is negative, but y (sine) is positive.
Quadrant III (180° to 270°)
Tangent & Cotangent are positive. Both x and y are negative, so their ratio is positive.
Quadrant IV (270° to 360°)
Cosine is positive. The x-coordinate is positive, but y is negative.
A Handy Mnemonic: "All Students Take Calculus"
- All: All functions are positive in Quadrant I.
- Students: Sine is positive in Quadrant II.
- Take: Tangent is positive in Quadrant III.
- Calculus: Cosine is positive in Quadrant IV.
Odd & Even Functions
Even Function: A function is even if f(-x) = f(x). The sign doesn't change for a negative angle.
Cosine is an even function: cos(-θ) = cos(θ).
Odd Functions: A function is odd if f(-x) = -f(x). The sign flips for a negative angle.
Sine, Tangent, and Cotangent are odd functions.
sin(-θ) = -sin(θ), tan(-θ) = -tan(θ)