Special Angles and Trig Functions (continued)

In class today we built on what we learned last class about the special angles and trig functions in the unit circle. We learned how to find the coordinates for a given point on the unit circle, and we also learned how to calculate the exact value of a trig function given with an angle, without using a calculator.

To find the coordinates for a point, P(θ), we must first convert the angle to degrees if it is given in radians, by multiplying by 180/pie. Next thing to do is draw out the special triangle that fits the angle. We should then set up a default point, (x, y), which is equal to (cosθ, sinθ). We then solve for cos (A/H) and sin (O/H), by using the length of the sides on the triangle. This should give the coordinate.

For example, to find the coordinates for P(pi/4):  pi/4 = 45°.



P(45°) = (x, y) = (cosθ, sinθ) = (cos45°, sin45°)

Cos = A/H = 1 /√2, Sin = O/H = 1/ √2.

= (1 / √2, 1 / √2)   is the answer (both remain positive since they are in Q. 1)

To find the exact value of a trig function with an angle, like tan120°:
We would draw the special triangle on the unit circle, which would look like the one below. Then we know: Tan = O/A = √3 / 1 = -√3 (since it is in Q. 2, tan becomes - )