Quadrant Signs (ASTC)
Which functions are positive in each quadrant.
Key idea
Which functions are positive in each quadrant.
In depth
The sign of each trig function depends on the quadrant: Q1 all positive, Q2 sine only, Q3 tangent only, Q4 cosine only (All Students Take Calculus). Signs follow from the signs of x and y.
Worked example
An angle of 210° is in Q3, so sin and cos are negative and tan is positive.
Real-world uses
- Checking the sign of a result in navigation or circuit calculations
- Remembering All Students Take Calculus
Common mistake
Forgetting the sign after finding a reference angle.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Quadrant Signs (ASTC)?
Which functions are positive in each quadrant. It is a topic at the intermediate level in Trigonometry.
Where is Quadrant Signs (ASTC) used in real life?
Real-world examples: Checking the sign of a result in navigation or circuit calculations; Remembering All Students Take Calculus.
What should I learn before Quadrant Signs (ASTC)?
Make sure you are comfortable with Reference Angles, the previous topic in Trigonometry.
What is a common mistake with Quadrant Signs (ASTC)?
Forgetting the sign after finding a reference angle.
How can I practise Quadrant Signs (ASTC)?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Quadrant Signs (ASTC)?
Move on to Coterminal Angles next.
Related intermediate topics in Trigonometry
- Radians – Angle measured by arc length on a unit circle; 2π rad = 360°.
- Converting Degrees and Radians – Multiply by π/180 or 180/π.
- Sine Ratio – Opposite over hypotenuse.
- Cosine Ratio – Adjacent over hypotenuse.
- Tangent Ratio – Opposite over adjacent.
- Reciprocal Trig Functions – Cosecant, secant and cotangent.