Reference Triangle

Please be patient while the Java applet loads.

Directions: Move slider θ in lower left-hand corner to move point P around the circle.

Did you notice:
The opposite side of right trianlge is always vertical (like y-axis).
The adjacent side of right trianlge is always horizontal (like x-axis).
The hypotenuse is the radius of the circle.

If the radius (hypotenuse) is 1, did you notice:
sin θ = y
cos θ = x
tan θ is slope (y/x or sin θ/cos θ)

Did you notice angle θ was restricted mostly to 0°, 30°, 45°, 60°, and 90°?

Find sin 90° and sin 270°. What is their relationship to y-axis?
Find cos 0° and cos 180°. What is their relationship to x-axis?

Find sin 0° and sin 180°. What is their relationship to x-axis?
Find cos 90° and cos 270°. What is their relationship to y-axis?

Find tan 90° and tan 270°. Why is it "?" or undefined?
Find tan 0° and tan 180°. Why is it zero?
What do you know about slopes of vertical and horzontal lines?
What do you know about tangent when vertical or horzontal?