Sinx is negative in the third quadrant; Sinx is negative in the fourth quadrant;

Cosx is positive in quadrant 1; Cosx in the second quadrant is negative;

Cosx in the third quadrant is negative; Cosx in the fourth quadrant is positive.

Sinx=y/r (quadrants 1 and 2, y is positive and quadrants 3 and 4 are negative)

Cosx=x/r (quadrants 1 and 4, where x is positive and quadrants 2 and 3 are negative).

Extended data:

Sine, a mathematical term, in a right triangle, the ratio of the opposite side to the hypotenuse of any acute angle ∠A is called sine of ∠A, which is abbreviated from the English word sine, that is, the opposite side/hypotenuse of Sina = ∠ A.

In ancient times, the "string" in "hook, three strands, four strings and five" was the hypotenuse of a right triangle, and "hook" and "strand" were the two right-angled sides of a right triangle. Sine = unit head/chord length

Trigonometric function is a kind of transcendental function in elementary function in mathematics. Their essence is the mapping between the set of arbitrary angles and a set of ratio variables. The usual trigonometric function is defined in the plane rectangular coordinate system, and its domain is the whole real number domain. The other is defined in a right triangle, but it is incomplete. Modern mathematics describes them as the limit of infinite sequence and the solution of differential equation, and extends their definitions to complex system.

Generally speaking, in rectangular coordinate system, given the unit circle, for any angle α, the vertex of the angle α coincides with the origin, the starting edge coincides with the non-negative semi-axis of the X axis, and the ending edge intersects with the unit circle at point P(u, v), so the ordinate V of the point P is called the sine function of the angle α, and it is recorded as v=sinα. Usually we use X to represent the independent variable, that is, X represents the size of the angle and Y represents the function value, so we define the trigonometric function of any angle y=sin.

X, its domain is all real numbers, and its value range is [- 1, 1].

Cosine (cosine function), a kind of trigonometric function. In Rt△ABC (right triangle), ∠ c = 90 (as shown in the figure), and the cosine of ∠A is the hypotenuse of the adjacent side of the triangle, that is, cosA=b/c, which can also be written as cosa=AC/AB. Cosine function: f(x)=cosx(x∈R).

The adjacent side of an angle is called the cosine of ∠A than the hypotenuse, and it is written as cosA (abbreviated as COSINE), that is, cosA= the adjacent side/hypotenuse of angle A (right triangle). The domain of cosine function written as cos a = x/r is a whole set of real numbers, and the range of values is [- 1, 1]. It is a periodic function with a minimum positive period of 2π. When the independent variable is 2kπ(k is an integer), the maximum value of the function is1; When the independent variable is (2k+ 1)π, the function has a minimum value of-1. Cosine function is an even function, and its image is symmetrical about y axis.

Baidu encyclopedia-sine function

Baidu encyclopedia-cosine function