Unit Circle

30° (C)

Say we plug in 30° as our angle measure. We would have 30/360=2π. 30/360 is 1/12, so we then have 1/12=2π. Then we can multiply 2π and 1/12 to get π/6. π/6 is 30° in radians. This same process can be used with all of the angles with measures of multiples of 30 or 45.

Radius of the Unit Circle (C)

The radius of the unit circle we are using is 1; the circumference for our unit circle is 2π.

Unit Circle (T)

There are 360 degrees in a circle, and the formula for the circumference of a circle is 2πr.

Graph of Cos (C)

This also relates to the equation we used earlier to get our degrees of angles into radians. We can use the measure of your selected angle in radians as the x coordinate. Then for the y coordinate, we use cos = x/r. So then we would use the x coordinates from out unit circle as the y coordinates of our cosine graph.

Graph of Tan (T)

This also relates to the equation we used earlier to get our degrees of angles into radians. We can use the measure of your selected angle in radians as the x coordinate. Then for the y coordinate, we use cos = y/x. So then we would use the special right triangle measures to find the values of the specific y/x equations. Then we can plus those values in as your y coordinates.

2π=360° (T)

This is the base equation to plug in certain angle measures. Using these angle measures a student can find the measure of the angle in radians.

Graph of Sin (T)

This relates to the equation we used earlier to get our degrees of angles into radians. We can use the measure of your selected angle in radians as the x coordinate, and the y coordinate from the unit circle for the y coordinate of your graph. You can do this same

Finding Coordinates (T)

To find all coordinates relative to your chosen angles, you should realize that the measures you are using are relative to special right triangles. Then you should use the rules relative to the special right triangles.

Finding the Cosine of your chosen angle (T)

With all the coordinates you have gathered in your unit circle, you can plug those coordinates of each angle to the equation of Cos. The equation of Cos is x over r. So, since you already know the x, y, and r of each angle, you can just plug it into equation of Cos and that will give you the Cos of your chosen angle.

Finding the Sine of your chosen angle (C)

With all the coordinates you have gathered in your unit circle, you can plug those coordinates of each angle to the equation of Sin. The equation of Sin is y over r. So, since you already know the x, y, and r of each angle, you can just plug it into equation of Sin and that will give you the Sin of your chosen angle.

Finding the Tangent of your chosen angle (C)

With all the coordinates you have gathered in your unit circle, you can plug those coordinates of each angle to the equation of Tan. The equation of Tan is y over x. So, since you already know the x, y, and r of each angle, you can just plug it into equation of Tan and that will give you the Tan of your chosen angle.