If the length of both sides of the included angle is known, the included angle can be calculated by trigonometric function. For example, if the length of the opposite side and the length of the adjacent side of the included angle are known, you can use the arctangent function (tan? ) to calculate the tangent value of the included angle, and then get the degree of the included angle through the inverse trigonometric function (arctan).
If two vectors of the included angle are known, the size of the included angle can be calculated by using the dot product of the vectors. The dot product of vectors is equal to the product of the modulus length of two vectors and the cosine of the included angle between them. The degree of included angle can be obtained by solving the inverse function of cosine (arccos).
If the length of both sides of the included angle and the length of the hypotenuse are known, the included angle can be calculated by Pythagorean theorem. Pythagorean theorem shows that the sum of squares of two sides of a triangle is equal to the square of the hypotenuse. By solving the inverse function (arcsin, arccos, arctan) in trigonometric function, the degree of included angle can be obtained.
Matters needing attention in calculating included angle
1, unit selection: the unit of included angle is usually degree and radian (rad), which unit needs to be clearly used in calculation. It should be noted that different mathematical and physical problems may have different requirements for units.
2. Expression of angle: The included angle can be expressed by angle system or arc system. The angle system takes 360 as a week, and the arc system takes the central angle of a circle with a radius equal to the arc length as a week. In the calculation, it is necessary to choose an appropriate representation according to specific problems.
3. Positive and negative angle: the angle can be positive (counterclockwise) or negative (clockwise), depending on the direction of rotation from the start edge to the end edge. In the calculation, it is necessary to determine the sign of the included angle according to the specific situation.
4. Calculation method of included angle: The calculation method of included angle depends on the specific situation. For right triangle, the included angle can be calculated by trigonometric functions such as sine, cosine and tangent. In other cases, it may be necessary to use vectors, coordinates or other geometric relationships to calculate the included angle.