Trig signs depend on the quadrant of the terminal side. Sine follows the y-coordinate sign, cosine follows the x-coordinate sign, and tangent follows their quotient.
⚠Angles on axes are special cases because some values can be zero or undefined.
How Trig Signs Work
After an angle is normalized, its quadrant determines the signs of sine, cosine, and tangent. This is often summarized by the ASTC rule.
Quadrant I
All three are positive.
Quadrant II
Only sine is positive.
Quadrant III
Only tangent is positive.
Quadrant IV
Only cosine is positive.
💡 Example: For 210°, the angle is in Quadrant III, so sin and cos are negative while tan is positive.
Applications of Trig Signs
ASTC RuleExact ValuesEquation SolvingGraphing
Frequently Asked Questions
What is a trig signs calculator?▼
It identifies whether sine, cosine, and tangent are positive or negative for an angle.
What is the ASTC rule?▼
ASTC means All positive in QI, Sine positive in QII, Tangent positive in QIII, Cosine positive in QIV.
How do I use this calculator?▼
Enter an angle in degrees and click Calculate.
What happens on the axes?▼
Axis angles may make some functions zero or undefined instead of simply positive or negative.
Where are trig signs used?▼
They are used in exact values, solving equations, graphing, and quadrant analysis.
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