How can we extend our concept of trig ratios to triangles that don't have a hypotenuse of 1 unit?
Drag point A along ray OC to make the triangle bigger or smaller. What kind of transformation maps the original triangle to the new triangle?
When you drag point A along ray OC, do the values of the trig ratios change? Why or why not?
Drag point C along the circle. Do the values of the trig ratios change? Why or why not?
On the previous page, you found that sine of [math]\alpha[/math] represents the length of the side opposite [math]\alpha[/math] in a triangle with a hypotenuse of 1. Change the length of the hypotenuse to something other than 1. How can you use the side lengths of the new triangle to find the sine of [math]\alpha[/math]?[br][br]Hint: Think about the transformation you selected in question 1. How does that transformation change the lengths of each side of the triangle?
On the previous page, you found that cosine of [math]\alpha[/math] represents the length of the side adjacent to [math]\alpha[/math] in a triangle with a hypotenuse of 1. How can you use the side lengths of the new triangle to find the cosine of [math]\alpha[/math]?
On the previous page, you found that tangent of [math]\alpha[/math] represents the length of the opposite side divided by the length of the adjacent side in a triangle with a hypotenuse of 1. How can you use the side lengths of the new triangle to find the tangent of [math]\alpha[/math]?