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Trigonometric Functions

Trigonometric Functions

 Table of Contents

Algebra II Terms

Get down with the lingo

Amplitude

How high can it go? Amplitude = max displacement.

Cofunction

Complementary 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: sin2ɵ + cos2ɵ = 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: a2 + b2 = c2. 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.

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