① Reciprocal relationship:

tanα cotα= 1？

sinα cscα= 1？

cosα secα= 1？

(2) business relationship:

tanα=sinα/cosα？

cotα=cosα/sinα？

③ Square relation:

sinα？ +cosα？ = 1?

1+tanα？ =secα

1+cotα？ =cscα？

Extended data:

You can also define six trigonometric functions according to the unit circle with the radius of 1 and the center of the circle as the origin. The definition of unit circle is of little value in practical calculation. In fact, for most angles, it depends on the right triangle. But the definition of the unit circle does allow trigonometric functions to define all positive and negative angles, not just in? 0? And then what? The angle between π/2 radians.

It also provides images containing all the important trigonometric functions. According to Pythagorean theorem, the equation of unit circle is: For any point on the circle (x, y), x? +y？ = 1。 Some common angles are measured in radians: counterclockwise is a positive angle, while clockwise is a negative angle. Let a straight line passing through the origin make an angle θ with the positive half of the X axis and intersect the unit circle.

The x and y coordinates of this intersection point are equal to cosθ and sinθ respectively. The triangle in the image ensures this formula; The radius is equal to the hypotenuse and the length is 1, so there is? sinθ=y/ 1？ And then what? Cosθ=x/ 1. The unit circle can be regarded as a way to view an infinite number of triangles by changing the lengths of adjacent sides and opposite sides, but keeping the hypotenuse equal to 1.

For greater than? 2π? Or less than or equal to 2π? Angle, you can continue to rotate directly around the unit circle. So sine and cosine become periodic? Periodic function of 2π: For any angle θ and any integer k.

Reference: trigonometric function (mathematical term) _ Baidu Encyclopedia