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# Trigonometric Functions

# Algebra II Terms

## Get down with the lingo

### Amplitude

How high can it go? Amplitude = max displacement.### Cofunction

*Co*mplementary functions. In a nutshell: cofunction A = function (A – 90°).

### 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 "hypos" are the biggest side of the right triangle. It's the side opposite the right angle in a right triangle.### Leg

They're kind of like people legs, but for triangles. They don't 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 maximum and minimum displacement.### 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

This guy gets us to the unit circle, in all of its glory: sin^{2}ɵ + cos

^{2}ɵ = 1. It will 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: a^{2}+ b

^{2}= c

^{2}. It's a way to find the leg or hypotenuse of a right triangle if the other two sides are known.

### Quadrant

Remember: "quad" means "4." So, a quadrant is just one fourth of coordinate plane. You see this word when talking about graphing on an*x*-

*y*plane, so it's not a totally new idea.

### Radian

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 the 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: Sin equals opposite side over hypotenuse. Cos equals adjacent side over hypotenuse. Tan equals opposite side over adjacent side.### Sum And Difference Identities

sin(α ± β) = sinαcosβ ± cosαβ cos(α±β) = cosαcosβ ∓ sinαsinβ### 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.### People who Shmooped this also Shmooped...

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