# Algebra II Terms

## Get down with the lingo

### Amplitude

How high can it go? A trig function's amplitude is the vertical distance between the midline and the maximum value.

### Cofunction

Complementary functions. In a nutshell: cofunction(A) = function(90° – A). For example, cos A = sin(90° – A).

### Cosecant

When 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.

### Cosine

In a right triangle, cosine equals an angle's adjacent leg over the hypotenuse. Also, it's the cofunction of sine.

### Cotangent

When 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.

### Hypotenuse

Looks 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.

### Leg

They'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.

### Midline

The middle of the road—the horizontal line halfway between the maximum and minimum values in a trig function.

### Period

This is how long it takes for one complete cycle. Up and down we go, where the sine function stops nobody knows.

### Periodic Function

A function that repeats over and over—think sine and cosine.

### Pythagorean Identity

The 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 Theorem

Thanks 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.

Remember: "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.

Think 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°.

### Reciprocal

A "flipped" or inverted fraction. Watch out for zeros in the denominator.

### Secant

We get this when cosine goes topsy-turvy. The reciprocal of the cosine function or just the cosine function flipped over.

### Sine

In a right triangle, sine equals an angle's opposite side over the hypotenuse. It's M. Night Shyamalan's favorite trig function.

### SOHCAHTOA

No, 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 Identities

A 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)

### Tangent

In a right triangle, tangent equals an angle's opposite side over its adjacent side.

### Trigonometry

Triangle + Measurement = It's just the study of right triangles.

### Unit Circle

"Un" means "1." A unit circle has a radius of one unit. It will be your best friend in calculus.