Definitions of Right Triangle Trigonometry
Right Triangle Math
I. Definitions of Right Triangle Trigonometric Functions.
A)
1) opp = opposite side, adj = adjacent side, hyp = hypotenuse
2) SOH – CAH – TOA
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.
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
II. Using the Pythagorean Theorem on the Unit Circle.
A) Pythagorean thm is a
2
+ b
2
= c
2
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 x
2
+ y
2
= r
2
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
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
The relationships between sides in a right triangle using trigonometric functions - sine, cosine, and tangent. Learn key mnemonic devices like SOH-CAH-TOA to easily recall these concepts for solving various mathematical problems.
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Presentation Transcript
Right Triangle Math I. Definitions of Right Triangle Trigonometric Functions. opp adj opp = = = A) cos tan sin hyp hyp 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 height width = = = sin tan cos width hyp hyp 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= c2for 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). y x y = = = sin cos tan r r x r r x = = = csc sec cot x y 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.
