Right Triangle Math I. Definitions of Right Triangle Trigonometric Functions. A) 1) opp = opposite side, adj = adjacent side, hyp = hypotenuse 2) SOH – CAH – TOA 3) Some Old Horse Came A-Hoppin’ Through Our Alley. B) If the right triangle is applied to the Unit Circle and written in standard form (the initial ray is on the x-axis), then … the height = y the width = x the radius = hypotenuse

Right Triangle Math II. Using the Pythagorean Theorem on the Unit Circle. A) Pythagorean thm is a2 + b2 = c2 for any right triangle. 1) If you know the (x , y) coordinates then you have the “a” and “b” terms in the Pyth thm. 2) The “a” (or “b”) term is the x (or y) coordinate, and the other letter is the other coordinate. 3) The “c” term is the hypotenuse [the “r” in the trig] B) If you know the coordinates for a given angle, you can use the Pythgorean theorem to find the hypotenuse (the r). 1) Now you can write all the trig functions using x, y, & r. C) The equation of a circle is x2 + y2 = r2 1) If you know any 2 numbers you can find the missing one. D) The angles of any triangle add up to be 180°.

Right Triangle Math III. The Six Trigonometric Functions on the Unit Circle. A) If you put the triangle on a Unit Circle in standard position, then you have these 6 trig identities (where hyp = radius). B) Reciprocal trig identities to sine, cosine and tangent are cosecent (csc), secant (sec) and cotangent (cot). 1) Reciprocal means to flip the fraction upside down.

Right Triangle Math