HOW DO YOU SOLVE THIS PROBLEM, sin theta>0,cos theta>0

You need to have those sin/cosine curves memorized. Do that now, flash cards work.

Draw them out now each on its own flashcard, and examine where both are positive.

You shouldn't have to ask this question, at your age.

Does theta represents a number?

If you have a scientific calculator, the cos and sin buttons are there for you to figure out this problem.

To solve the problem, we want to find the values of θ that satisfy both sin θ > 0 and cos θ > 0.

First, let's recall the unit circle. In the unit circle, the x-coordinate represents cos θ and the y-coordinate represents sin θ. Since sin θ > 0, we know that the y-coordinate is positive. Similarly, since cos θ > 0, we know that the x-coordinate is positive.

Now, we can divide the unit circle into four quadrants:

- In the first quadrant, both sin θ and cos θ are positive.
- In the second quadrant, sin θ is positive while cos θ is negative.
- In the third quadrant, both sin θ and cos θ are negative.
- In the fourth quadrant, sin θ is negative while cos θ is positive.

Since we are looking for solutions where both sin θ and cos θ are positive, we need to focus on the first quadrant.

In the first quadrant, θ ranges from 0 to 90 degrees (or 0 to π/2 radians). So, the values of θ that satisfy sin θ > 0 and cos θ > 0 are all the angles between 0 and π/2 radians (or 0 and 90 degrees) in the first quadrant.

To summarize, the solution to the problem is:
θ ∈ (0, π/2) or θ ∈ (0, 90°).