Graph sin(theta)>0 , tan(theta)<0

Problem

sin(θ)>0,tan(θ)<0

Solution

1. Identify the quadrants where sin(θ)>0 The sine function is positive in the first and second quadrants (0<θ<π.

2. Identify the quadrants where tan(θ)<0 The tangent function is negative in the second and fourth quadrants (π/2<θ<π and (3*π)/2<θ<2*π.

3. Determine the intersection of these two conditions. The only quadrant where both sin(θ)>0 and tan(θ)<0 are true is the second quadrant.

4. Define the interval for the second quadrant. In terms of radians, this is π/2<θ<π In terms of degrees, this is 90<θ<180

Final Answer

Quadrant II⇒90<θ<180

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