Sine function:
For any real number x, it corresponds to a unique angle (equal to this real number in the radian system), and this angle corresponds to the uniquely determined sine value sin x. Thus, for any real number x, there is a uniquely determined value sin x and It corresponds to the function established according to this corresponding law, expressed as f(x)=sin x, called a sine function.
The theorem of sine function: in a triangle, the ratio of each side to its diagonal sine is equal, that is, a/sin A=b/sin B=c/sin C.
In the right triangle ABC, ∠C = 90°, y is a right angle side, R is an oblique side, X is another right angle side (in the coordinate system, this is the base), then sin A=y/r,r=√(x^2+y^2).
Cosine function:
Cosine = hook length/chord length
Put the Pythagorean string in the circle. A chord is a line of two points on the circumference. The biggest chord is the diameter. If the string of a right triangle is placed on the diameter, the strand is the long string, that is, the sine, and the hook is the short string, that is, the remaining chord, the cosine.
In modern terms, a sine is the ratio of the opposite side to the hypotenuse of a right triangle.
The modern sine formula is to put an angle into a rectangular coordinate system so that the starting edge of the angle coincides with the non negative half axis of the X axis.
Find a point a (x, y) on the final edge of the angle to make the vertical line of X axis through a, then r=(x^2+y^2)^(1/2).
cos =x/r
The cosine has a maximum value of 1 and a minimum value of -1.
Tangent function
Tangent function is a right triangle, the ratio of the opposite side to the adjacent side is called tangent. In a rectangular coordinate system.
Tan takes an angle and returns the ratio of the two right sides of a right triangle. This ratio is the ratio of the length of the opposite side of the angle to the length of the adjacent side in a right triangle.
Therefore, before the 1990s, the tangent function is expressed in terms of TG θ, and after the 1990s, it is expressed in terms of Tan θ.
Cotangent function:
Cot + angle is used for cot+angle, for example: cot30° is cot30°, the cotangent of angle a is expressed as cotA.
If the abscissa of any point on the final edge of an angle is divided by the non-zero ordinate of the point, the vertex of the angle coincides with the origin of the plane rectangular coordinate system, and the beginning edge of the angle coincides with the positive x-axis.
Cotangent and tangent are reciprocal of each other.
In a right triangle, the ratio of the adjacent right angles and the relative right angles of an acute angle is called the cotangent of the acute angle.
Secant function:
Let △ABC, ∠C = 90° (middle school is a trigonometric function with acute angle) AC=b，BC=a，AB=c，∪[1,+∞)) secant function: sec∠A=c/b(bevel/adjacent edge)，y=secx.
In y = secx, take any value of X that makes secx meaningful and its corresponding y value as (x, y). The graph made in rectangular coordinate system is called secant function image, also known as secant curve.
Trigonometric function:
Trigonometric functions (also known as "circle functions") are functions of angles; they are important in studying triangles and modeling periodic phenomena and in many other applications. A trigonometric function is usually defined as the ratio of the two sides of a right triangle containing the angle, or the length of various line segments on the unit circle. More modern definitions express them as solutions of infinite series or specific differential equations, allowing them to be extended to any number of positive and negative values, even complex values.
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