# Oriented angles and polar locating : 11th grade math lesson

A math lesson for 11th grade on oriented angles and polar. In this lesson, we will discuss sine, cosine and tangent with the different trigonometric relations.

## I. Locating on the trigonometric circle.

### 1. winding on the numerical right.

Definition: trigonometric circle.

The trigonometric circle is the circle with center O and radius 1.

It has a direction of travel called direct, which is counter-clockwise.

With this choice, we say that the plane is oriented.

Ownership:

Any real number has a single image point on the circle If it exists such as then and have the same image point on the circle .

Definition:

The radian measure of an angle is equal to the length of the arc of the trigonometric circle that it intercepts.

Ownership:
The measurements of the angles in radian and degree are proportional.

## II. Measurements of an oriented angle.

Definition: oriented angle.

Let and be two non-zero vectors and the points M and N such that and are their respective representatives of origin O. Let M’ and N’ be the points of intersection of the half-lines [OM) and [ON) with the trigonometric circle.

Let x and y be two real numbers that have image points M’ and N’, then y-x is a radian measure of the oriented angle .

Property: main measure.
The angle oriented has a single measure in the interval called the principal measure of the angle.
Properties:
1. Chasles relation for angles: let , and be three non-zero vectors, then .
2. Characterization of the collinearity of two vectors: two vectors and are collinear if, and only if, .
Properties:

Let and be two non-zero vectors.

1. ;

## III. Cosine and sine of a real and of an oriented angle.

### 1. Locating using cosine and sine.

Theorem : coordinates of a point of the trigonometric circle.

let x be a real number and M its image point on the trigonometric circle . The point M has coordinates .

Properties:

For any real x and any relative integer k.

1. (Pythagorean theorem).

Particular values:

### 2. The associated angles.

Properties:

For any real number x :

Properties:

For any real number x :

1. .
2. .
3. .
4. .

### 3. Duplication formulas.

Properties:

Consider two real numbers a and b.

1. .
2. .
3. .
4. .
Properties:

Consider a real number a.

1. .
2. .

Cette publication est également disponible en : Français (French) Español (Spanish) العربية (Arabic)

## Other forms similar to oriented angles and polar locating : 11th grade math lesson.

• 98
The equations and inequations of the second degree in a math lesson for 11th grade where we will approach the resolution with the delta discriminant and the factorization of a polynomial of the second degree as well as the study of its sign. In this first lesson, we will study…
• 98
A eleventh math lesson on the limits of functions and the existence of an asymptote to the representative curve of this function. The limits of functions and the study of horizontal, vertical and oblique asymptotes in a 11th grade math lesson where we will discuss the definition of the asymptote…
• 97
Probability in a 11th grade math lesson where we will study the law of large numbers and the law of probabilities. In this first grade lesson, we will also cover the concept of equiprobability, the expectation and standard deviation and the variance of a random variable. I. Random variables and…

Les dernières fiches mises à jour.

Voici les dernières ressources similaires à oriented angles and polar locating : 11th grade math lesson mis à jour sur Mathovore (des cours, exercices, des contrôles et autres), rédigées par notre équipe d'enseignants.

On Mathovore, there is 13 703 923 math lessons and exercises downloaded in PDF.

Categories Uncategorized
Mathovore

FREE
VIEW