Solve the System of @WORD sin(x)<0 , cos(x)>0

Problem

sin(x)<0,cos(x)>0

Solution

1. Identify the quadrants in the Cartesian plane where the sine function is negative. The condition sin(x)<0 occurs in Quadrant III and Quadrant IV.

2. Identify the quadrants where the cosine function is positive. The condition cos(x)>0 occurs in Quadrant I and Quadrant IV.

3. Determine the intersection of these two conditions. The only quadrant where both sin(x)<0 and cos(x)>0 are true is Quadrant IV.

4. Express the solution in terms of the standard interval for Quadrant IV. In the interval [0,2*π) this corresponds to (3*π)/2<x<2*π

5. Generalize the solution to account for the periodicity of the trigonometric functions by adding 2*k*π where k is any integer.

Final Answer

(3*π)/2+2*k*π<x<2*π+2*k*π,k∈ℤ

Want more problems? Check here!