If you need to calculate the angle of inclination of a straight line to the x-axis, and you don't know the equation of the line, omit from any point of the line (except the point of intersection with the axis) perpendicular to the axis. Then measure the other two sides received a right triangle and find the ratio of adjacent side to the opposite. The resulting number will be equal to the tangent of the angle of inclination. This method is useful not only to explore the angle of inclination of a straight line, but also to measure any angles, as in the drawing, and in life (for example, the angle of the slope of the roof).
If you know the equation of the line and you need to find the tangent of the angle of inclination of this straight line to the x-axis, Express through H. as a result, you will get an expression of type y=KX+b. Note the k-factor is the tangent of the angle of inclination between the positive direction of x-axis and the beam direct located need this axis. If k=0, the tangent is also zero, then there is a direct parallel to or coincides with the abscissa axis.
If you are given a complicated function such as a quadratic, and you need to find the tangent of the angle of inclination of the tangent to this function, or, in other words, the angle coefficient, and calculate the derivative. Then calculate the value of the derivative at a given point, which will be held tangent. The resulting number is the tangent of the angle of inclination of the tangent. For example, you are given the function y=x^2+3x, the derivative, you will get an expression y`=2x+3. To find the slope at x=3, substitute this value into the equation. As a result of simple calculations it is easy to obtain y=2*3+3=9, this is the desired tangent.
To find the tangent of the angle of inclination of one side of the triangle to another, proceed as follows. Find the sine (sin) of that angle and divide it by the cosine (cos), you get the tangent of that angle.
Advice 2 : How to calculate the angle
The calculation of the angle of inclination may be needed to solve a variety of problems – the calculation of the slope of the roof, countertops, installing solar panels, antennas, pipes, etc. in addition, often the angle of slope we need to find the drawing – it could be the slope of the straight relative to the plane, the angle of inclination of the tangent, etc. anyway, a search algorithm is the same for any task.
You will need
- - plumb
- - level;
Try to build a rightanglespacious treanglethe parts mentally, with rods or cords, drawing pencil, depending on working conditions. Importantly, one of the angles of frictionangleof the parts was equal to 90⁰, and the inclined plane appeared in the quality of the hypotenuse, that is, the longest side lying opposite the right angle.
If possible, use gravity - it's the easiest way. For example, continue the sloping line to the ground or floor, and the lower string with the load. Measure the distance between the cargo and the point of intersection of the inclined line with the ground.
To calculate the angle of inclination of a river or road, determine the elevation at the beginning and end of the object. For example, the highest point lies at an altitude of 100 meters above sea level, and the lower one at a height of 40 meters (elevation define the map or level). In the example shown, the vertical leg is equal to 60 meters, and the length of an object decide on the map or by using direct measurements (length of road can be determined by the car speedometer).
Transfer the measurements to a sheet of paper. Schematically depict treanglethe parts, indicate the size of each side. Divide the length of the vertical leg to the length of the inclined line. The resulting number – the sine of the desired angle. Grab a calculator (you can use the online calculator) and entering the obtained value, click the arc sine (asin). You will receive the angle of inclination in degrees.
You may be unable to calculate the length of the inclined side. In this case, divide the length of the vertical (opposite) sides of the length of the horizontal (adjacent). You will get the tangent of the angle of tiltto calculate the angle in degrees, find its arctangent using a calculator.
If you work with a drawing and you need to find the slope of the straight line, try to determine its equation. Knowing the coordinates of two points, use the formula (x-x1)/(x2-x1)=(u-U1)/(U2-U1). Substitute the coordinates and give the equation to the form y=kx+b. The k coefficient in front of x is the tangent of the angle of inclination of a straight line. To find the angle of inclination, calculate its tangent.