For the first activity, only slide the [b]SINE [/b]slider to conceptually see the meaning of the Sine ratio within this right triangle context. Once you have completed all 6 activities below, repeat the process, but use the COSINE slider.[br][br]Before you begin your work on the activities, spend a few minutes interacting with the applet. You can move the 2 LARGER WHITE VERTICES of the triangle anywhere you'd like. The black ACUTE ANGLE slider (or input box below it) is used to change the size of angle [math]\alpha[/math] . Then see below for instructions.

[b]EXPLORATORY QUESTION[/b]S[br][br][color=#0000ff][b]1. [/b][/color][br]What does the triangle look like when the sliders (Sine and acute angle) are set to the far left? [br]Sketch what you see. [br]Explain the relative sizes (hypotenuse, adjacent leg, and opposite leg).[br]Now move the SINE slider to the far right. [br]Write down what appears in the upper left corner. Explain the meaning of this.[br][br][color=#38761d][b]2.[/b][/color][br]Reset the SINE slider to the far left.[br]Adjust the acute slider to 15 degrees.[br]Sketch what you see.[br]Now move the SINE slider to the far right.[br]Sin(15[math]^\circ[/math] ) is approximately equal to what value?[br]Explain what the value means in terms relative sizes of the legs.[br]The _________ leg is ____% as long as the ____________.[br][br][color=#ff0000][b]3.[/b][/color][br]Reset the SINE slider to the far left.[br]Adjust the acute angle so that it's 30 degrees.[br]Sketch what you see.[br]Explain the numerical values and words in the upper left corner.[br]The _________ leg is ____% as long as the ___________.[br][br][color=#ff7700][b]4.[/b][/color][br]Reset the SINE slider to the far left.[br]Set the acute angle to 45 degrees.[br]Sketch what you see.[br]Move the SINE slider to the right and explain what the Sin (45 ) means.[br]The ______ leg is ___% as long as the ___________.[br][br][b][color=#ffff00]5. [/color][/b][br]Reset the SINE slider to the far left.[br]Set the acute angle so that it's 60 degrees.[br]Sketch what you see.[br]Move the SINE slider to the right and explain what the Sin ( ) means.[br]The ______ leg is ___% as long as the ____________.[br][br][color=#783f04][b]6. [/b][/color][br]Reset the SINE slider to the far left.[br]Set the acute angle to 85, 86, 87, 88, 89, and 90 degrees.[br]Can you sketch what you see?[br]Move the SINE slider to the right and explain what the Sin (90 ) means.[br]The ______ leg is ___% as long as the ____________.[br][br][br]Repeat the same 6 activities, BUT use COSINE instead of SINE.