Trigonometric functions are really important in math, especially in geometry and calculus. They help us understand angles and shapes better. These functions behave differently depending on where you are on the graph, which is called the Cartesian plane. Let's break it down by the four quadrants:

1. Sine (sin):

   • Quadrant I: Positive (This means $\sin \theta > 0$)
   • Quadrant II: Positive ($\sin \theta > 0$)
   • Quadrant III: Negative ($\sin \theta < 0$)
   • Quadrant IV: Negative ($\sin \theta < 0$)

2. Cosine (cos):

   • Quadrant I: Positive ($\cos \theta > 0$)
   • Quadrant II: Negative ($\cos \theta < 0$)
   • Quadrant III: Negative ($\cos \theta < 0$)
   • Quadrant IV: Positive ($\cos \theta > 0$)

3. Tangent (tan):

   • Quadrant I: Positive ($\tan \theta > 0$)
   • Quadrant II: Negative ($\tan \theta < 0$)
   • Quadrant III: Positive ($\tan \theta > 0$)
   • Quadrant IV: Negative ($\tan \theta < 0$)

4. Cosecant (csc): This is the opposite of sine. It has the same sign as sine.

5. Secant (sec): This is the opposite of cosine. It has the same sign as cosine.

6. Cotangent (cot): This is the opposite of tangent. It has the same sign as tangent.

So, here’s a quick summary:

• In Quadrant I, all functions are positive.
• In Quadrant II, sine and cosecant are positive.
• In Quadrant III, tangent and cotangent are positive.
• In Quadrant IV, cosine and secant are positive.

Knowing how these functions change in different quadrants helps a lot when you are solving trigonometric problems or looking at periodic functions.