[b]Goal:[/b][br]Demonstrate why trigonometric function names change and signs reverse when using the vertical Y-axis (270°) as a reference.[br][br][b]Description:[/b][br]Just like at 90°, the 270° line is a vertical reference. This means the triangle "tips over" again, causing the "Opposite" and "Adjacent" sides to swap roles. Therefore, Sine becomes Cosine. However, in the 3rd and 4th quadrants, we must also carefully check the coordinate signs.[br][br][b]Instructions:[br][/b][br]1. Set the slider [icon]/images/ggb/toolbar/mode_slider.png[/icon] to an angle between 180° and 360° (eg: 240°).[br][br]2. Think of the negative Y-axis (270°) as your new reference line.The gray angle shows how far your angle is from 270°.So the angle is rewritten as (270+-x) (e.g: 270 - 30⁰)[br][br]3. Focus on the right triangle formed by this gray angle near the 270° reference axis.[br][list][*]Examine the sides of this small triangle?[/*][*]What is the length of the vertical side, sin(x)?[/*][*]What is the length of the horizontal side, cos(x)?[/*][*]How do these compare to the sides of the original large-angle triangle?[/*][/list]4. Use your observations to guess which function value (sin or cos) the small triangle’s sides now represent.[br][br]5. Determine how the signs of sine and cosine change when the angle is in 3rd or 4th Quadrant.[br][br]6. Check the equations of on the sides different angles and to observe how your findings occur.