Draw a unit circle. Be sure to label the radius and axes.

  1. Label an angle Ө of your choice
  2. Label the lengths sin Ө and cos Ө

Draw two right triangles. Make them look like similar triangles. Label the sides with all possible sine and cosine values.

  1. Triangle MNQ: hypotenuse = 1 and one angle is Ө
  2. Triangle XYZ: hypotenuse = A and the “same” angle is Ө

Now, divide the length NQ by MN. Perform the same operation on the corresponding sides of triangle XYZ. Set each of these values as tan Ө. Does the value of tan Ө change with the size of the triangle?

How does your definition of tan Ө apply to the unit circle? Draw a new, better unit circle with this new value labeled.

Challenge: Instead of angle Ө, draw a 30, 60, or 45 degree angle and compute all lengths and remaining angles in the resulting right triangle.

Practice problems: Compute the following values using a unit circle.

  1. tan 45 = ______________________
  2. sin 30 = ______________________
  3. cos 30 = ______________________
  4. sin 60 = ______________________
  5. cos 60 = ______________________
  6. sin 45 = ______________________
  7. cos 45 = _____________________