Graph sin(theta)>0

Problem

sin(θ)>0

Solution

1. Identify the period of the sine function, which is 2*π

2. Determine the intervals within one period [0,2*π] where the sine function is positive.

3. Observe that sin(θ)=0 at θ=0,π,2*π

4. Analyze the quadrants where the ycoordinate on the unit circle is positive, which occurs in Quadrant I and Quadrant II.

5. Conclude that sin(θ)>0 when 0<θ<π

6. Generalize the solution for all real numbers by adding multiples of the period 2*k*π where k is any integer.

Final Answer

sin(θ)>0⇔2*k*π<θ<(2*k+1)*π,k∈ℤ

Want more problems? Check here!