Course Project Unit Circle
Now that we've learned how to use right triangle trigonometry, let's extend our knowledge so that we can use these relationships on any angle measure (not just acute angles). Consider the following applet. The circle drawn has radius = 1
If we form a right triangle using the radius as the hypotenuse notice what happens to the trigonometric functions of this triangle.
If we form a right triangle using the radius as the hypotenuse notice what happens to the trigonometric functions of this triangle.
- Record your observations.
- Use algebra to give another expression for tangent in terms of sine and cosine.
- Give alternate representations for sine, cosine, and tangent using the x and y values of the triangle's point on the circle.
- Consider the right triangle with two 45 degree angles. Use the Pythagorean theorem and the fact that the triangle is isosceles to show the value of both legs. Don't forget to rationalize the denominator! Verify your answer by setting the angle to 45 degrees.
- What did the video tell you about other angle measures?
- Verify these by setting the angle to those specific angle measures in the applet below.
- Why does this work when angles are not acute?
- Find other angle measures in this applet which show a specific value for the ratios.
- Why do these ratios look familiar?
- Create your own unit circle and fill in the values for those coordinates.