The Unit Circle and Trigonometric Properties

1. Move the slider in upper left of the graphics view. Take note of the movement of the point P around the circle as the angle increase. Click “Reset” to set angle back to 0˚.   2. Set the angle to 45˚ and use the mnemonic “SOH CAH TOA” to verify that the opposite and adjacent lengths are sin(θ) and cos(θ) respectively. Why is the hypotenuse always 1?   3. Move the slider to the following angles and take note of the x and y coordinates of the point P (below slider): 45˚; 90˚; 120˚; 250˚; 300˚ Use a calculator (set to degrees) to verify that sin(θ) and cos(θ) correspond to the coordinates of P. Make conjectures about the coordinates and the lengths of the opposite and adjacent sides.   4. Verify that the green length Observe what happens to the tangent when θ= 90˚, 180˚, 270˚, 360˚. Make conjectures about the values in your solutions.   5. Use the results of (3) to verify that mnemonic CAST (Cosine – All – Sine – Tangent) holds positive in their respective quadrants.   6. Click on a check box of a desired function then click “Animate” to see the graph of the function. Make note of the behavior of each function.