if sin 0 > 0 and tan 0 < 0, what quadrant contains the terminal side of 0.
The sine is positive in I and II quadrant,negative in III and IV quadrant.
The tangent is positive in I and III guadrant,negative in II and IV quadrant.
If sin(theta)>0 sine is positive
If tan(theta)<0 tangent is negative
Only quadrant where sine is positive,and tangent is negative is quadrant II.
To determine the quadrant containing the terminal side of angle 0, we need to consider the signs of sine and tangent.
Given that sin 0 > 0 (sin 0 is positive) and tan 0 < 0 (tan 0 is negative), we can deduce the following:
- In the unit circle, the sine function is positive in the first and second quadrants.
- The tangent function is negative in the second and fourth quadrants.
Since both sine and tangent have different signs (sine is positive, and tangent is negative), the angle 0 must lie in the second quadrant.
To determine which quadrant contains the terminal side of an angle, you need to look at the signs of the trigonometric functions in that quadrant.
Since sin(0) = 0, and sin(0) > 0, we know that the angle 0 lies on the x-axis. This means it passes through Quadrant I and Quadrant II.
Next, we need to examine the sign of the tangent function. Since tan(0) = sin(0) / cos(0) = 0 / 1 = 0, we see that tan(0) is equal to 0. However, the important information is that tan(0) < 0.
Since tan(0) < 0, this tells us that the sign of tan(0) is negative. In the unit circle, negative values for tan are found in the third and fourth quadrants.
Combining the information, we can conclude that the angle 0 lies in Quadrant IV because it lies on the x-axis and the value of tan(0) is negative, which corresponds to Quadrant IV.