Unit circle quadrant 4 Quiz - Free Printable

To fill in the unit circle, we need to determine two things for each point:
1. The Angle: Measured in degrees starting from the right side (0°) and going counter-clockwise.
2. The Coordinates: Written as $(x, y)$, which correspond to $(\cos \theta, \sin \theta)$.

Here is the step-by-step breakdown of the values you need to write in the blanks. The circle is divided into increments of $30^\circ$ and $45^\circ$.

Step 1: The "Easy" Points (Axes)

These are the points that lie directly on the horizontal and vertical lines. Their coordinates are always $0$, $1$, or $-1$.

* Right ($0^\circ$):
* Angle: $0^\circ$ (or $360^\circ$)
* Coordinate: $(1, 0)$
* Top ($90^\circ$):
* Angle: $90^\circ$
* Coordinate: $(0, 1)$
* Left ($180^\circ$):
* Angle: $180^\circ$
* Coordinate: $(-1, 0)$
* Bottom ($270^\circ$):
* Angle: $270^\circ$
* Coordinate: $(0, -1)$

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Step 2: Quadrant I (Top Right)

*Angles between $0^\circ$ and $90^\circ$. Both x and y are positive.*

* $30^\circ$:
* Coordinate: $\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$
* $45^\circ$:
* Coordinate: $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$
* $60^\circ$:
* Coordinate: $\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$

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Step 3: Quadrant II (Top Left)

*Angles between $90^\circ$ and $180^\circ$. x is negative, y is positive.*

* $120^\circ$:
* Coordinate: $\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$
* $135^\circ$:
* Coordinate: $\left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$
* $150^\circ$:
* Coordinate: $\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$

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Step 4: Quadrant III (Bottom Left)

*Angles between $180^\circ$ and $270^\circ$. Both x and y are negative.*

* $210^\circ$:
* Coordinate: $\left(-\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)$
* $225^\circ$:
* Coordinate: $\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$
* $240^\circ$:
* Coordinate: $\left(-\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)$

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Step 5: Quadrant IV (Bottom Right)

*Angles between $270^\circ$ and $360^\circ$. x is positive, y is negative.*

* $300^\circ$:
* Coordinate: $\left(\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)$
* $315^\circ$:
* Coordinate: $\left(\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$
* $330^\circ$:
* Coordinate: $\left(\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)$

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Final Answer:

Here is the complete list of values to fill in the circles, moving counter-clockwise starting from the rightmost point ($0^\circ$):

1. $0^\circ$: $(1, 0)$
2. $30^\circ$: $\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$
3. $45^\circ$: $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$
4. $60^\circ$: $\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$
5. $90^\circ$: $(0, 1)$
6. $120^\circ$: $\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$
7. $135^\circ$: $\left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$
8. $150^\circ$: $\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$
9. $180^\circ$: $(-1, 0)$
10. $210^\circ$: $\left(-\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)$
11. $225^\circ$: $\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$
12. $240^\circ$: $\left(-\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)$
13. $270^\circ$: $(0, -1)$
14. $300^\circ$: $\left(\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)$
15. $315^\circ$: $\left(\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$
16. $330^\circ$: $\left(\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)$