The unit circle is called the "unit" circle because it has a radius of 1.

null

1

What is the length of the radius of the unit circle?

1

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

What is the coordinate point at 180° ?
Type your answer as an ordered pair (x,y).

1

What is the coordinate point at 270° ?
Type your answer as an ordered pair (x,y).

1

What is the coordinate point at 2\pi radians ?
Type your answer as an ordered pair (x,y).

1

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?

These are the different angles a painter uses for portraits

These are the angles in the special right triangles

I have never seen these angles before in my life

These are the camera angles a photographer uses

1

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

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!

null

Recall how to set up the table for 30-60-90

null

1

What is the exact value of x?
No decimal answers so you must use the table above!

1

What is the exact value of y?
No decimal answers so you must use the table above!

1

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?

30\degree

45°

60°

90°

1

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

Use the 45-45-90 table to find exact value of x.
No decimals and remember to rationalize the denominator!

1

Use the same table to find exact value of y.
No decimals and remember to rationalize the denominator!

1

We have ONE more coordinate point to find in Quadrant 1.
Which reference angle does the last missing point represent?

30\degree

45°

60°

90°

1

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

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?

The base (x) and height (y) will turn negative.

The base (x) and height (y) will be the same as the 30° reference angle.

The base (x) and height (y) will switch from the the 30\degree reference angle.

1

List the values in order from least to greatest.

1

On the unit circle on your Radians worksheet, write in the coordinate points for Quadrants 1 and 2.

null

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

The coordinate point for \frac{\pi }{6} in Q1 is
What is the coordinate point for \frac{5\pi }{6} in Q2?

1

When you list out the coordinate points in Quadrant III, what do you think will happen to the signs of the values?

Both the x-value and y-value will be positive. (+,+)

The x-value will be positive but y-value will be negative. (+,-)

Both the x-value and y-value will be negative. (-,-)

1

The coordinate point for \frac{\pi }{4} in Q1 is
What is the coordinate point for \frac{5\pi }{4} in Q3?

1

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

Match the correct signs of each coordinate point (x,y) for each Quadrant.

(+,+)
(-,-)
(-,+)
(+,-)

Quadrant I
Quadrant II
Quadrant III
Quadrant IV

1

The coordinate point for \frac{\pi }{3} in Q1 is
What is the coordinate point for \frac{5\pi }{3} in Q4?

null

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!

Coordinate Points on the Unit Circle

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!

Coordinate Points on the Unit Circle

The unit circle is called the "unit" circle because it has a radius of 1.

What is the length of the radius of the unit circle?

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).

What is the coordinate point at 180° ?Type your answer as an ordered pair (x,y).

What is the coordinate point at 270° ?Type your answer as an ordered pair (x,y).

What is the coordinate point at 2\pi radians ?Type your answer as an ordered pair (x,y).

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?

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?

If the radius of the unit circle is 1, what is the length of the hypotenuse of this triangle?

What is the exact value of x?No decimal answers so you must use the table above!

What is the exact value of y?No decimal answers so you must use the table above!

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?

Looks like we found 3 of the 5 coordinate points in Quadrant 1.

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?

Use the 45-45-90 table to find exact value of x.No decimals and remember to rationalize the denominator!

Use the same table to find exact value of y.No decimals and remember to rationalize the denominator!

We have ONE more coordinate point to find in Quadrant 1. Which reference angle does the last missing point represent?

We have ONE more coordinate point to find in Quadrant 1.

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?

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?

List the values in order from least to greatest.

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.

The coordinate point for \frac{\pi }{6} in Q1 is What is the coordinate point for \frac{5\pi }{6} in Q2?

When you list out the coordinate points in Quadrant III, what do you think will happen to the signs of the values?

The coordinate point for \frac{\pi }{4} in Q1 is What is the coordinate point for \frac{5\pi }{4} in Q3?

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

Match the correct signs of each coordinate point (x,y) for each Quadrant.

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!

The unit circle is called the "unit" circle because it has a radius of 1.

What is the length of the radius of the unit circle?

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).

What is the coordinate point at 180° ?Type your answer as an ordered pair (x,y).

What is the coordinate point at 270° ?Type your answer as an ordered pair (x,y).

What is the coordinate point at 2\pi radians ?Type your answer as an ordered pair (x,y).

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?

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?

If the radius of the unit circle is 1, what is the length of the hypotenuse of this triangle?

What is the exact value of x?No decimal answers so you must use the table above!

What is the exact value of y?No decimal answers so you must use the table above!

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?

Looks like we found 3 of the 5 coordinate points in Quadrant 1.

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?

Use the 45-45-90 table to find exact value of x.No decimals and remember to rationalize the denominator!

Use the same table to find exact value of y.No decimals and remember to rationalize the denominator!

We have ONE more coordinate point to find in Quadrant 1. Which reference angle does the last missing point represent?

We have ONE more coordinate point to find in Quadrant 1.

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?

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?

List the values in order from least to greatest.

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.

The coordinate point for \frac{\pi }{6} in Q1 is What is the coordinate point for \frac{5\pi }{6} in Q2?

When you list out the coordinate points in Quadrant III, what do you think will happen to the signs of the values?

The coordinate point for \frac{\pi }{4} in Q1 is What is the coordinate point for \frac{5\pi }{4} in Q3?

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

Match the correct signs of each coordinate point (x,y) for each Quadrant.

The coordinate point for \frac{\pi }{3} in Q1 is What is the coordinate point for \frac{5\pi }{3} in Q4?

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).

What is the coordinate point at 180° ?
Type your answer as an ordered pair (x,y).

What is the coordinate point at 270° ?
Type your answer as an ordered pair (x,y).

What is the coordinate point at 2\pi radians ?
Type your answer as an ordered pair (x,y).

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?

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?

What is the exact value of x?
No decimal answers so you must use the table above!

What is the exact value of y?
No decimal answers so you must use the table above!

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?

Use the 45-45-90 table to find exact value of x.
No decimals and remember to rationalize the denominator!

Use the same table to find exact value of y.
No decimals and remember to rationalize the denominator!

We have ONE more coordinate point to find in Quadrant 1.
Which reference angle does the last missing point represent?

The coordinate point for \frac{\pi }{6} in Q1 is
What is the coordinate point for \frac{5\pi }{6} in Q2?

The coordinate point for \frac{\pi }{4} in Q1 is
What is the coordinate point for \frac{5\pi }{4} in Q3?

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}

The coordinate point for \frac{\pi }{3} in Q1 is
What is the coordinate point for \frac{5\pi }{3} in Q4?

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).

What is the coordinate point at 180° ?
Type your answer as an ordered pair (x,y).

What is the coordinate point at 270° ?
Type your answer as an ordered pair (x,y).

What is the coordinate point at 2\pi radians ?
Type your answer as an ordered pair (x,y).

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?

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?

What is the exact value of x?
No decimal answers so you must use the table above!

What is the exact value of y?
No decimal answers so you must use the table above!

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?

Use the 45-45-90 table to find exact value of x.
No decimals and remember to rationalize the denominator!

Use the same table to find exact value of y.
No decimals and remember to rationalize the denominator!

We have ONE more coordinate point to find in Quadrant 1.
Which reference angle does the last missing point represent?

The coordinate point for \frac{\pi }{6} in Q1 is
What is the coordinate point for \frac{5\pi }{6} in Q2?

The coordinate point for \frac{\pi }{4} in Q1 is
What is the coordinate point for \frac{5\pi }{4} in Q3?

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}

The coordinate point for \frac{\pi }{3} in Q1 is
What is the coordinate point for \frac{5\pi }{3} in Q4?