[b]Goal:[/b] Demonstrate why trigonometric function names remain the same when using the horizontal X-axis (180°) as a reference.[br][br][b]Description:[/b][br][br]When we measure an angle from the horizontal X-axis, the triangle acts like a mirror reflection across the Y-axis. The “Opposite” side (vertical) stays vertical, and the “Adjacent” side (horizontal) stays horizontal. Because the roles of the sides do not swap, the function name stays the same.[br][br][b]Instructions:[br][/b][list=1][*]Set the slider [icon]/images/ggb/toolbar/mode_slider.png[/icon] to an angle between 90° and 270° (e.g., 120°).[/*][*]Notice that the applet shows x-axis as your reference line.[br]It is calculating how far your angle is from 180°. [br]The angle is rewritten as (180+-x) (e.g: 180 - 60⁰).[br][br][/*][*]You will see the same [b]x angle[/b] drawn in the 1st quadrant as a simple right triangle.[br][br][/*][*][b]Compare the two triangles[/b][br]Look at the triangle in the 1st quadrant and look at the triangle of the (180-+x) angle.[br]Which sides corresponds to [b]sin(x)[/b]?[br]Which sides corresponds to [b]cos(x)[/b]?[br][br][/*][*]Determine how the signs of sine and cosine change when the angle is in Quadrant II and Quadrant III.[br][br][/*][*]Check the equations of on the sides different angles and to observe how your findings occur.[br][/*][/list][br]

[i][color=#999999][size=150]Write your answers in the given space below each question. Use complete mathematical expressions.[/size][/color][/i]