Algebra II Terms
Get down with the lingo
AmplitudeHow high can it go? A trig function's amplitude is the vertical distance between the midline and the maximum value.
CofunctionComplementary functions. In a nutshell: cofunction(A) = function(90° – A). For example, cos A = sin(90° – A).
CosecantWhen the sine function goes topsy-turvy. Reciprocal of the sine function or just the sine function flipped over. Also, it's the cofunction of secant.
CosineIn a right triangle, cosine equals an angle's adjacent leg over the hypotenuse. Also, it's the cofunction of sine.
CotangentWhen the tangent function goes topsy-turvy. Reciprocal of the tangent function or just the tangent function flipped over. Also, it's the cofunction of tangent.
HypotenuseLooks a little like the word hippo, so remember hippos are big and the "hypo" is the biggest side of the right triangle. It's the side opposite the right angle.
LegThey're kind of like people legs, but for triangles. They just won't be caught dead in jeggings. Two legs hold the hypotenuse up. It's also a side opposite an acute angle in a right triangle.
MidlineThe middle of the road—the horizontal line halfway between the maximum and minimum values in a trig function.
PeriodThis is how long it takes for one complete cycle. Up and down we go, where the sine function stops nobody knows.
Periodic FunctionA function that repeats over and over—think sine and cosine.
Pythagorean IdentityThe trig version of the Pythagorean Theorem. It looks like this, in all of its glory: sin2 ɵ + cos2 ɵ = 1. It'll come in handy for the rest of your math life. Learn to love it.
Pythagorean TheoremThanks to our buddy Pythagoras, we can know all kinds of stuff about triangles using this theorem: a2 + b2 = c2. It's a way to find the leg or hypotenuse of a right triangle if the other two sides are known.
QuadrantRemember: "quad" means "4." So, a quadrant is just one-fourth of the coordinate plane. You see this word when talking about graphing on an x-y plane, so it's not a totally new idea.
RadianThink of our radiant sun; it looks like a full circle of 360° (or 2π) from Earth. A radian is just another way to measure angles: 2π radians = 360°.
ReciprocalA "flipped" or inverted fraction. Watch out for zeros in the denominator.
SecantWe get this when cosine goes topsy-turvy. The reciprocal of the cosine function or just the cosine function flipped over.
SineIn a right triangle, sine equals an angle's opposite side over the hypotenuse. It's M. Night Shyamalan's favorite trig function.
SOHCAHTOANo, this is not an alien's mumblings, it's just an easy way to remember your trig definitions: Sine equals Opposite side over Hypotenuse. Cosine equals Adjacent side over Hypotenuse. Tangent equals Opposite side over Adjacent side.
Sum And Difference IdentitiesA set of special formulas that let us find the sine or cosine of two angles added together or subtracted. They look like this:
sin(α ± β) = sin(α)cos(β) ± cos(α)sin(β)
cos(α ± β) = cos(α)cos(β) ∓ sin(α)sin(β)