1. 1. acute trigonometric function

The sine, cosine and exact sum of the acute angle A are called trigonometric function ∠ A.

If ∠a is the acute angle of Rt△ABC, then there is

1.2. Calculation of acute trigonometric function

1.3. Solving Right Triangle

In a right triangle, the process of finding other edges and angles from some known edges and angles is called solving a right triangle.

2. The positional relationship between a straight line and a circle

2. 1. Position relationship between straight line and circle

When a straight line and a circle have two common points, it is called the intersection of the straight line and the circle; When a straight line and a circle have a common point, it is said that the straight line is tangent to the circle, and the common point is called the tangent point; When a straight line and a circle have no common point, it is called separation of straight line and circle.

The positional relationship between a straight line and a circle has the following theorems:

A theorem to determine the tangency between a straight line and a circle;

The straight line passing through the outer end of the radius and perpendicular to the radius is the tangent of the circle.

Tangent property of circle:

The radius passing through the tangent point is perpendicular to the tangent of the circle.

2.2. Tangent Length Theorem

We usually call the length of the line segment from a point outside the circle to the tangent point the tangent length.

Tangent Length Theorem: The lengths of two tangents of a circle made through a point outside the circle are equal.

2.3. The inscribed circle of a triangle

A circle tangent to all three sides of a triangle is called the inscribed circle of the triangle, the center of the circle is called the heart of the triangle, and the triangle is called the circumscribed circle of the circle. The center of a triangle is the intersection of three bisectors of the triangle.

3. Three views and surface development diagram

3. 1. Inference

The shadow formed by an object in a certain plane under the irradiation of light is called projection. The ray is called the projection line, and the plane where the projection is located is called the projection plane. The projection formed by parallel projection lines is called parallel projection.

The light of the sun and searchlight can be regarded as parallel light, and the projection they form is parallel projection.

3.2. Three Views of Simple Geometry

The orthographic projection of an object on the orthographic projection plane is called the front view, the orthographic projection on the horizontal projection plane is called the top view, and the orthographic projection on the side projection plane is called the left view.

Front view, left view and top view are collectively called three views.

The direction of the projection line that produces the main view is also called the main view direction.

3.3. Geometry is described by three views.

Three views not only reflect the shape of the object, but also reflect the size in all directions.

3.4. Surface expansion diagram of simple geometry

The plane figure obtained by "cutting" geometry along some edges and connecting faces together is called the surface expansion diagram of geometry.

A cylinder can be regarded as a geometric body, which is surrounded by a rectangular ABCD rotating around one side BC and a surface formed by other sides. The curved surface formed by the rotation of AB and CD is two bottom surfaces of a cylinder and two circles with the same radius. The surface formed by AD rotation is the side of the cylinder, and it is the generatrix of the cylinder no matter where AD rotates.

A cone can be regarded as a geometric body formed by the rotation of a right triangle ACB around one of its right-angled sides (AC). The surface formed by right-angle BC rotation is the bottom surface of the cone, and the surface formed by hypotenuse AB rotation is the side surface of the cone. No matter where the hypotenuse AB rotates, it is called the generatrix of the cone.