If it is even, the function name remains the same.
If it is an odd number, it becomes its complementary function (sine and cosine transform, sine and cotangent transform, sine and cotangent transform).
Take α as an acute angle (note that it is "regarded"), and take the sign of trigonometric function according to the quadrant of the obtained angle.
2. According to the professional statement, in Kπ/2, if k is even, the function name is unchanged, and if it is odd, the function name becomes the opposite function name.
See the symbol of the quadrant where α is in the original function.
There is a formula about symbols:
One is all positive, two are sine, three are tangent and four are cosine.
That is, the first quadrant is all positive, the second quadrant sine is positive, the third quadrant tangent cotangent is positive, and the fourth quadrant cosine is positive.
Or ASTC for short, that is, all, sin, tan+cot and cos are positive in turn.
It can also be abbreviated as: the right tan/cot diagonal of cos on sin, that is, the positive values of sin are all above the X axis, the positive values of cos are all on the right side of the Y axis, and the positive values of tan/cot are oblique.
References:
Trigonometric function, expert contribution
Trigonometric function is one of the basic elementary functions, which takes the angle (the most commonly used radian system in mathematics, the same below) as the independent variable, and the angle corresponds to the coordinates where the terminal edge of any angle intersects with the unit circle or its ratio as the dependent variable.
It can also be equivalently defined as the lengths of various line segments related to the unit circle.
Trigonometric function plays an important role in studying the properties of geometric shapes such as triangles and circles, and is also a basic mathematical tool for studying periodic phenomena.
In mathematical analysis, trigonometric function is also defined as the solution of infinite series or specific differential equation, which allows its value to be extended to any real value or even complex value.
Common trigonometric functions are sine function, cosine function and tangent function.
Other trigonometric functions, such as cotangent function, secant function, cotangent function, dyadic function, cofactor function, semidyadic function and semifactorial function, are also used in other disciplines, such as navigation, surveying and engineering.
The relationship between different trigonometric functions can be obtained by geometric intuition or calculation, which is called trigonometric identity.