I. Sine formula
Sine formula is sin(x) = opposite side/hypotenuse, or it can be expressed as sin (x) = b/c, where x is an acute angle, the opposite side is the right side corresponding to x in a right triangle, and the hypotenuse is the right side perpendicular to the opposite side in a right triangle, that is, c is the hypotenuse of a right triangle.
Second, the cosine formula
Cosine formula is cos(x) = adjacent side/hypotenuse, or it can be expressed as cos (x) = a/c, where x is an acute angle and the adjacent side is the right side corresponding to x in a right triangle, that is, A is the adjacent side of a right triangle.
Third, the tangent formula
The tangent formula is tan(x) = opposite side/adjacent side, which can also be expressed as tan (x) = b/a, where x is an acute angle and the opposite side is the right side corresponding to x in a right triangle, that is, b is the opposite side of a right triangle.
Four, cotangent formula
Cotangent formula is cot(x) = adjacent side/opposite side, or COT (x) = a/b, where X is an acute angle, and the adjacent side is the right side corresponding to X in the right triangle, that is, A is the adjacent side of the right triangle.
The relationship between the sum of squares of sine and cosine of verb (verb abbreviation)
The sum of squares of sine and cosine can be expressed as sin? (x) + cos？ (x) = 1. This relationship can be used to verify whether the calculation results of sine and cosine are correct.
Sixth, the complementary relationship between sine and cosine.
The complementary relationship between sine and cosine can be expressed as cos(x) =-sin(π/2-x), that is, cos(x) =-tan(π/2-x). If the lengths of the opposite side and the hypotenuse of an acute angle are known, this relation can be used to solve the acute angle.
Properties and applications of trigonometric functions
1 and the application of trigonometric functions?
Trigonometric functions are widely used in mathematics, physics, engineering and other fields. For example, in geometry, trigonometric functions can be used to calculate angles and lengths; In physics, trigonometric functions can be used to describe physical phenomena such as vibration and fluctuation. In engineering, trigonometric functions can be used to design bridges, buildings and other structures.
2. What are the properties of trigonometric functions?
Trigonometric functions have some important properties, such as periodicity: the period of sine and cosine functions is 2π, that is, they are repeated every 2π angle. Boundedness: the range of sine and cosine functions is between-1 and 1, that is, their range of values is bounded.
Symmetry: the sine function takes the value of 0 on the axis of symmetry, and the cosine function takes the value of 1 or-1 on the axis of symmetry, that is, they all have symmetry.