The table below lists different angles within a circle.
1 Fill in the rows for 12, 9, and 6 o’clock, converting between hours, degrees, and radians.
2 Fill in the rows for 1:30, 10:30, 7:30, and 4:30, converting between hours, degrees, and radians.
Remember: degrees and radians both start with zero at "3 o’clock", and increase in the opposite direction of the hours!
We’ve filled in the rows for 12:00 and 3:00, as well as the length columns.
| Time | θ Degrees | θ Radians | x | y |
|---|---|---|---|---|
3:00 |
0° |
0π |
1 |
0 |
1:30 |
$$\displaystyle \sqrt{2} \over\displaystyle 2$$ |
$$\displaystyle \sqrt{2} \over\displaystyle 2$$ |
||
12:00 |
90° |
$$\displaystyle {2 \over\displaystyle 4}\pi$$ |
0 |
1 |
10:30 |
-$$\displaystyle \sqrt{2} \over\displaystyle 2$$ |
$$\displaystyle \sqrt{2} \over\displaystyle 2$$ |
||
9:00 |
-1 |
0 |
||
7:30 |
-$$\displaystyle \sqrt{2} \over\displaystyle 2$$ |
-$$\displaystyle \sqrt{2} \over\displaystyle 2$$ |
||
6:00 |
0 |
-1 |
||
4:30 |
$$\displaystyle \sqrt{2} \over\displaystyle 2$$ |
-$$\displaystyle \sqrt{2} \over\displaystyle 2$$ |
||
3:00 |
360° |
$$\displaystyle {8 \over\displaystyle 4}pi$$ |
1 |
0 |
3 In Pyret, experiment the functions sin and cos, passing in different radian values from the table above.
a. Which function computes x(θ)?
b. Which function computes y(θ)?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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