Examples of quadrants in the following topics:
-
- In quadrant II, “Smart,” only sine is positive.
- Reference angles in quadrant I are used to identify which value any angle in quadrants II, III, or IV will take.
- For any given angle in the first quadrant, there is an angle
in the second quadrant with the same sine value.
- For any angle in quadrants II, III, or IV, there is a reference angle in quadrant I.
- For any angle in quadrants II, III, or IV, there is a reference angle in quadrant I.
-
- The third quadrant has both negative x and y coordinates.
- Point $(4,0)$ is on the x-axis and not in a quadrant.
- Point $(0,-2)$ is on the y-axis and also not in a quadrant.
- The four quadrants of a Cartesian coordinate system.
- The four quadrants of a Cartesian coordinate system.
-
- The x- and y-axes
divide the coordinate plane (and the unit circle, since it is centered at the origin) into four quarters called quadrants.
- We
label these quadrants to mimic the direction a positive angle would
sweep.
- The four quadrants are labeled I, II, III, and IV.
-
- Notice how the sine values are positive between $0$ and $\pi$, which
correspond to the values of the sine function in quadrants I and II on
the unit circle, and the sine values are negative between $\pi$ and $2\pi$, which correspond to the values of the sine function in quadrants III and IV on the unit circle.
-
- Recall that different signs are applied to trigonometric functions that fall in each of the four quadrants (according to the mnemonic rule "A Smart Trig Class").
- Notice that we used only the positive root because $15^{\circ}$$$ falls in the first quadrant and $\sin(15^{\circ})$ is therefore positive.
-
- If we know the quadrant where the angle
is, we can easily choose the correct solution.