Download Some Old Horse Came A

Right Triangle Trigonometry
I. Definitions of Right Triangle Trigonometric Functions.
A)
opp
sin  
hyp
adj
cos  
hyp
opp
tan  
adj
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 …
height
sin  
hyp
width
cos  
hyp
the height = y
the width = x
tan  
height
width
the radius = hypotenuse
Right Triangle Trigonometry
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 Trigonometry
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).
sin  
y
r
r
csc  
y
cos  
x
r
r
sec  
x
tan  
y
x
x
cot  
y
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 Trigonometry