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 where the sine function is negative within one full rotation [0,2*π)

3. Recall that sin(θ) represents the ycoordinate on the unit circle, which is negative in the third and fourth quadrants.

4. Find the specific range for θ by noting that sin(θ)=0 at θ=π and θ=2*π

5. Express the solution as a set of intervals, accounting for the periodicity by adding 2*π*k where k is any integer.

6. Visualize the graph of y=sin(θ) and identify the regions where the curve lies below the horizontal θaxis.

Final Answer

π+2*π*k<θ<2*π+2*π*k,k∈ℤ

Want more problems? Check here!