identify all possible quadrants of an angle theta that satisifies the given conditions sin theta>0, cos theta>0

To determine the possible quadrants for the angle \(\theta\) given the conditions \(\sin \theta > 0\) and \(\cos \theta > 0\), let's analyze the sine and cosine values across the four quadrants:

1. **Quadrant I**: 
   - \(\sin \theta > 0\)
   - \(\cos \theta > 0\)
   
   Both conditions are satisfied in the first quadrant.

2. **Quadrant II**: 
   - \(\sin \theta > 0\)
   - \(\cos \theta < 0\)

   Here, only sine is positive, but cosine is negative, so this does not satisfy the given conditions.

3. **Quadrant III**: 
   - \(\sin \theta < 0\)
   - \(\cos \theta < 0\)
   
   Both sine and cosine are negative, so this does not satisfy the given conditions.

4. **Quadrant IV**: 
   - \(\sin \theta < 0\)
   - \(\cos \theta > 0\)

   In this quadrant, cosine is positive, but sine is negative, so this does not satisfy the given conditions.

From this analysis, we can see that the only quadrant where both \(\sin \theta > 0\) and \(\cos \theta > 0\) is true is **Quadrant I**.

### Answer:
The possible quadrant for \(\theta\) is **Quadrant I**.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. What are the signs of \(\tan \theta\) in each quadrant?
2. How can you determine the quadrant of an angle based on the signs of its trigonometric functions?
3. What are the conditions for \(\cos \theta > 0\) and \(\tan \theta < 0\)?
4. How do the unit circle and its coordinates relate to the values of sine and cosine?
5. What are the values of \(\sin \theta\) and \(\cos \theta\) at special angles like \(0^\circ\), \(90^\circ\), \(180^\circ\), and \(270^\circ\)?

**Tip:** The sign of a trigonometric function in a specific quadrant can help you quickly determine which quadrant an angle belongs to without calculating its exact value.

Identify all possible quadrants of an angle theta that satisfies the given conditions sin theta > 0, cos theta > 0.

Explore which quadrant an angle theta belongs to when sin theta > 0 and cos theta > 0. This guide covers the analysis of trigonometric functions and their signs across the four quadrants, helping students identify the correct quadrant for these conditions. Suitable for high school students in Grades 9-12.

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