Unit 4circles And Areawelcome

Unit 4 Circles And Area Welcome Rotonda
Unit 4 Circles And Area Welcome Table
Unit 4 Circles And Area Welcome Page

Understand and apply theorems about circles MGSE9-12.G.C.1 Understand that all circles are similar. MGSE9-12.G.C.2 Identify and describe relationships among inscribed angles, radii, chords, tangents.

What is the unit circle?

Winking Unit 4-3 page 97. Find the most appropriate value for ‘x’ in each of the diagrams below. (Assume point ‘A’ is the center of the circle.). Unit 4 Reference Sheet Name: Circle: The set of points in a plane that are fixed distance from a given point called the center of the circle. Chord: A segment whose endpoints both lie on the same circle. Radius: A segment whose endpoints are the center of a circle and a point on the circle. Learn circles unit 8 with free interactive flashcards. Choose from 500 different sets of circles unit 8 flashcards on Quizlet.

1 Answer

Explanation:

In mathematics, a unit circle is a circle with a radius of one. In trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.

The point of the unit circle is that it makes other parts of the mathematics easier and neater. For instance, in the unit circle, for any angle θ, the trig values for sine and cosine are clearly nothing more than sin(θ) = y and cos(θ) = x. ... Certain angles have 'nice' trig values.

The circumfrence of the unit circle is #2pi#. An arc of the unit circle has the same length as the measure of the central angle that intercepts that arc. Also, because the radius of the unit circle is one, the trigonometric functions sine and cosine have special relevance for the unit circle.

What is the Unit Circle?

Well, the Unit Circle, according to RegentsPrep, is a circle with a radius of one unit, centered at the origin.

Why make a circle where the radius is 1, you may ask?

If the radius is a length of 1, then that means that every Reference Triangle that we create has a hypotenuse of 1, which makes it so much easier to compare one angle to another.

Reference Triangle in the First Quadrant of the Unit Circle

But, the Unit Circle is more than just a circle with a radius of 1; it is home to some very special triangles.

Remember, those special right triangles we learned back in Geometry: 30-60-90 triangle and the 45-45-90 triangle? Don’t worry. I’ll remind you of them.

45-45-90 Triangle

Well, these special right triangles help us in connecting everything we’ve learned so far about Reference Angles, Reference Triangles, and Trigonometric Functions, and puts them all together in one nice happy circle and allow us to find angles and lengths quickly.

In other words, the Unit Circle is nothing more than a circle with a bunch of Special Right Triangles.

Now, I agree that may sound scary, but the cool thing about what I’m about to show you is that you don’t have to draw triangles anymore or even have to create ratios to find side lengths.

The Unit Circle

Everything you see in the Unit Circle is created from just three Right Triangles, that we will draw in the first quadrant, and the other 12 angles are found by following a simple pattern! In fact, these three right triangles are going to be determined by counting the fingers on your left hand!

How to Memorize the Unit Circle

Ok, so there are two ways you can do this:

Use a Unit Circle Chart
Simply know how to count

If it were me, I’d just want to count and not have to memorize a table, and that’s what I’m going to show you.

The Unit Circle has an easy to follow pattern, and all we have to do is count and look for symmetry. Moreover, everything you need can be found on your Left Hand.

If you place your left hand, palm up, in the first quadrant your fingers mimic the special right triangles that we talked about above: 30-60-90 triangle and the 45-45-90 triangle.

I will show you how to remember each angle, in radian measure, for each of your fingers and also how to find all the other angles quickly by using the phrase:

All Students Take Calculus!

For a quick summary of this technique, you can check out my Unit Circle Worksheets below.

And after you know your Radian Measures, all we have to do is learn an amazing technique called the Left-Hand Trick that is going to enable you to find every coordinate quickly and easily.

Furthermore, this Left-Hand Trick is going to help you not only to memorize the Unit Circle, but it is also going to allow you to evaluate or find all six trig functions!

Additionally, as Khan Academy nicely states, the Unit Circle helps us to define sine, cosine and tangent functions for all real numbers, and these ratios (that we have sitting in the palm of our hand) be used even with circles bigger or smaller than a radius of 1.

Isn’t that awesome?

Yes, indeed!

As you’re watching the video, you’re going to learn how to: