Use similar triangles to define, in any right triangle with hypotenuse z, the trigonometric function as cos0= x/z sin0= y/z tan0 = y/x Hint: The cirle has a radius 1.I am not exactly sure on how...

Use similar triangles to define, in any right triangle with hypotenuse z, the trigonometric function as cos0= x/z sin0= y/z tan0 = y/x

Hint: The cirle has a radius 1.

I am not exactly sure on how to answer this question.

embizze | Certified Educator

Begin with the unit circle centered at the origin of the cartesian coordinate plane. Draw a ray with endpoint (0,0) that intersects the circle at the point (x,y). From (x,y) drop a perpendicular segment to the x-axis. Connect the origin to the intersection of the perpendicular segment and the x-axis. You will have a right triangle.

Consider the angle at the origin, call it `theta` ; also name the hypotenuse `z` . (Note that since this is a unit circle, z=1). The side opposite `theta` is the vertical leg, and it has length `|y|` , while the horizontal segment adjacent to `theta` has length `|x|` .