[Test] Basic Trigonometry (powered by Wikipedia)

In course we will investigate basic trigonometry functions.

Introduction

Unit circle

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In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions[1][2]) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

The most familiar trigonometric functions are the sine, cosine, and tangent. In the context of the standard unit circle (a circle with radius 1 unit), where a triangle is formed by a ray starting at the origin and making some angle with the x-axis, the sine of the angle gives the length of the y-component (the opposite to the angle or the rise) of the triangle, the cosine gives the length of the x-component (the adjacent of the angle or the run), and the tangent function gives the slope (y-component divided by the x-component).

What is sin

Sin is  of unit circle point.e^{ix} = \cos x + i \sin x

Choose something

Definitions

Sine and cosine

Sine

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. The word comes from the Latin sinus for gulf or bay,[3] since, given a unit circle, it is the side of the triangle on which the angle opens. In our case:

Cosine

The cosine (sine complement, Latin: cosinussinus complementi) of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse, so called because it is the sine of the complementary or co-angle, the other non-right angle.[4] Because the angle sum of a triangle is π radians, the co-angle B is equal to π/2 − A; so cos A = sin B = sin(π/2 − A). In our case:

An illustration of the relationship between sine and its out-of-phasecomplement, cosine. Cosine is identical, but π/2 radians out of phase to the left; so cos A = sin(A + π/2).

Choose right definition

  • sine
    the ratio of the length of the adjacent side to the length of the hypotenuse
  • cosine
    the ratio of the length of the opposite side to the length of the hypotenuse

Untitled fill in the blanks question

\frac{opposite}{hypotenuse}

is

\frac{adjacent}{hypotenuse}is