2. The second quadrant: sine is positive, cosine is negative and tangent is negative.
3. The third quadrant: sine is negative, cosine is negative and tangent is positive.
4. The fourth quadrant: sine is negative, cosine is positive and tangent is negative.
Simply summarized as: one is all positive, the other is sine, the third is tangent, and the fourth is cosine.
The six angles of a hexagon represent six kinds of trigonometric functions respectively, and they are related as follows:
1) The diagonal product is 1, that is, sinθ cscθ =1; cosθsecθ= 1； tanθ cotθ= 1 .
2) A trigonometric function represented by any three adjacent vertices of a hexagon, and the function value in the middle position is equal to the product of two adjacent function values, such as: sin θ = cos θ tan θ; tanθ=sinθ secθ ...
3) The sum of the squares of the top two vertices of the triangle in the shaded part is equal to the square value of the bottom vertex, such as: .
Extended data:
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. That is, "Like a finite number, the symbol looks at the quadrant" (or "Even if it changes singularly, the symbol looks at the quadrant").
In Kπ/2, if k is even, the function name remains the same, 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, the other is sine, the third is tangent and the fourth is cosine, that is, the first quadrant is all positive, the second quadrant is all sine, the third quadrant is all cotangent and the fourth quadrant is all cosine.
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.
For example: 90+α. Naming: 90 is an odd multiple of 90, and the complementary function should be taken; Note: If α is regarded as an acute angle, then 90+α is the second quadrant, and the sine of the second quadrant is positive and the cosine is negative. So SIN (90+α) = COS α, COS (90+α) =-SIN α, which is amazing and works well ~
Another formula is "vertical variation and horizontal variation, and the sign depends on the quadrant", for example: SIN (90+α), the terminal edge of 90 is on the vertical axis, so the function name becomes the opposite function name, that is, cos, so SIN (90+α) = COS α.