sin37 =3/5

tan37 =sin37 /cos37 =3/4

In a right triangle, when the connecting lines AB, AC and BC of three points A, B and C on the plane form a right triangle, where ∠ACB is a right angle. For ∠BAC, the opposite side A = BC, the hypotenuse) c=AB, and the adjacent side B = AC.

In the plane rectangular coordinate system xOy, let the starting edge of ∠ β be the positive semi-axis of the X axis, let point P(x, y) be any point on the final edge of ∠βthat does not coincide with the origin O, let r=OP, and let ∠β = ∠ α, then:

,,? ,,? ,。

Extended data:

The trigonometric function of odd multiples of 90+α and the absolute value of α trigonometric function are complementary. The trigonometric function of even multiples of 90+α is the same as the absolute value of α. That is, "odd parity is the same, odd parity is the same."

Numbering rules:

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.

References:

Baidu encyclopedia-trigonometric function