The unit circle is called the "unit" circle because it has a radius of 1.
1 point
1
Question 1
1.
What is the length of the radius of the unit circle?
1 point
1
Question 2
2.
When the unit circle is drawn over an x- and y-axis it has some important coordinate points (x,y) along the edge of the circle.
What is the coordinate point at 90\degree?
Hint: Look at the image above.
Type your answer as an ordered pair (x,y).
1 point
1
Question 3
3.
What is the coordinate point at 180° ?
Type your answer as an ordered pair (x,y).
1 point
1
Question 4
4.
What is the coordinate point at 270° ?
Type your answer as an ordered pair (x,y).
1 point
1
Question 5
5.
What is the coordinate point at 2\pi radians ?
Type your answer as an ordered pair (x,y).
1 point
1
Question 6
6.
What's the coordinate point at 30\degree? __________
To find the coordinate point at 30° we can create a right triangle with the 30° reference angle.
Keep scrolling to see how!
1 point
1
Question 7
7.
We're going to be drawing triangles inside the unit circle, using the special angles of the unit circle.
These are the special angles of the unit circle:
Where else have you seen these angles?
1 point
1
Question 8
8.
Let's take a closer look at ONLY the 30\degree angle in Quadrant I.
If we draw a vertical line from the edge of the circle down to the x-axis it creates a right triangle:
What is the measure of the missing angle at the top of the triangle?
1 point
1
Question 9
9.
If the radius of the unit circle is 1, what is the length of the hypotenuse of this triangle?
Now we need to find the two missing side lengths x and y using the 30-60-90 special right triangle ratios.
You cannot use sin or cos because we need exact fractions, no decimals!
Recall how to set up the table for 30-60-90
1 point
1
Question 10
10.
What is the exact value of x?
No decimal answers so you must use the table above!
1 point
1
Question 11
11.
What is the exact value of y?
No decimal answers so you must use the table above!
1 point
1
Question 12
12.
The x-value and y-value you just found make up the coordinate point (x,y) for the 30\degree angle on the unit circle.
Notice how the __________ of the triangle represents the x-value of the point and the __________ of the triangle represents the y-value of the point on the circle.
Since the __________ of the triangle is the radius of the circle, that will always be __________
1 point
1
Question 13
13.
Looks like we found 3 of the 5 coordinate points in Quadrant 1.
Let's find the other two! Which reference angle does the middle point in Q1 represent?
1 point
1
Question 14
14.
If we create a right triangle with the 45\degree reference angle, what is the measure of the missing angle at the top of the triangle?
1 point
1
Question 15
15.
Use the 45-45-90 table to find exact value of x.
No decimals and remember to rationalize the denominator!
1 point
1
Question 16
16.
Use the same table to find exact value of y.
No decimals and remember to rationalize the denominator!
1 point
1
Question 17
17.
The x-value and y-value you just found make up the coordinate point (x,y) for the 45\degree angle on the unit circle.
Notice how the __________ of the triangle represents the x-value of the point and the __________ of the triangle represents the y-value of the point on the circle.
Since the __________ of the triangle is the radius of the circle, that will always be __________
1 point
1
Question 18
18.
We have ONE more coordinate point to find in Quadrant 1.
Which reference angle does the last missing point represent?
1 point
1
Question 19
19.
If we create a right triangle with the 60\degree reference angle, what is the measure of the missing angle at the top of the triangle?
1 point
1
Question 20
20.
Notice that we have another 30-60-90 triangle, except the 30\degree and 60\degree angles switched places. How do you think that will effect the base (x) and height (y) of the triangle?
1 point
1
Question 21
21.
If you were to find x and y using the 30-60-90 table,
you would find that the values do in fact __________ from the 30\degree reference angle
1 point
1
Question 22
22.
List the values in order from least to greatest.
1 point
1
Question 23
23.
Start at 0\degree and rotate up counter-clockwise.
As the angles in the unit circle increase:
- the x-value starts at 1 and gets __________ until x=0 at 90\degree. This is because the __________ of the right triangles we drew got smaller and smaller.
- the y-value starts a 0 and gets __________ until y=__________ at 90°. This is because the __________ of the right triangles we drew got taller and taller.
On the unit circle on your Radians worksheet, write in the coordinate points for Quadrants 1 and 2.
Notice how the reference angle (denominator) determines the coordinate points.
For example, the \frac{\pi }{3} reference angles in Q1 and Q2 have similar values.
1 point
1
Question 24
24.
Notice how the coordinate points in Quadrant 2 are the same as Quadrant 1, except now all of the __________ are negative.
1 point
1
Question 25
25.
The coordinate point for \frac{\pi }{6} in Q1 is
What is the coordinate point for \frac{5\pi }{6} in Q2?
1 point
1
Question 26
26.
When you list out the coordinate points in Quadrant III, what do you think will happen to the signs of the values?
1 point
1
Question 27
27.
The coordinate point for \frac{\pi }{4} in Q1 is
What is the coordinate point for \frac{5\pi }{4} in Q3?
1 point
1
Question 28
28.
The coordinate point for \frac{\pi }{4} in Q1 is
What is the coordinate point for \frac{7\pi }{4} in Q4?
Hint: think about if the x-value or y-value would be negative in Quadrant IV
1 point
1
Question 29
29.
Match the correct signs of each coordinate point (x,y) for each Quadrant.
(+,-)
(-,-)
(+,+)
(-,+)
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
1 point
1
Question 30
30.
The coordinate point for \frac{\pi }{3} in Q1 is
What is the coordinate point for \frac{5\pi }{3} in Q4?
Fill in the rest of the coordinate points all around the unit circle on your worksheet. Raise your hand when you're done so I can check your work!