Coplanar lines are lines that lie on the same plane. In other words, any two points on each of the lines can be connected with a straight line that lies entirely in the same plane. For example, if two lines intersect, they are coplanar because the plane containing one line also contains the other line.…
Skew lines are two non-intersecting lines that are not parallel to each other. In other words, skew lines are two lines in three-dimensional space that do not lie in the same plane and do not intersect each other. Skew lines are important in geometry and can be used to solve various problems, such as finding…
The distance between two points in three-dimensional space can be found using the following formula: d = √((x2 – x1)^2 + (y2 – y1)^2 + (z2 – z1)^2) where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two points, and d is the distance between them. To use the formula, you…
To find the equation of a circle passing through the points of intersection of two circles, we can follow these steps: Let’s say the two circles have equations: (x – a)^2 + (y – b)^2 = r^2 (x – c)^2 + (y – d)^2 = s^2 where (a,b) and (c,d) are the centers of the…
Suppose we have two lines in a Cartesian coordinate system, given by the equations: a1x + b1y + c1 = 0a2x + b2y + c2 = 0 The angle between these two lines can be found using the formula: tan(theta) = |(m2 – m1)/(1 + m1*m2)| where m1 and m2 are the slopes of the…
To find the equation of a line passing through the point of intersection of two given lines, you can follow these steps: Note: If the two given lines are parallel, they will never intersect, and there will be no point of intersection. In this case, it is not possible to find a line passing through…
In analytical geometry, the distance between two points in a plane is given by the distance formula: d = sqrt((x2 – x1)^2 + (y2 – y1)^2) where (x1, y1) and (x2, y2) are the coordinates of the two points and d is the distance between them. To use the formula, simply substitute the values of…
Here are some of the commonly used trigonometric formulas involving multiple and sub-multiple angles: These formulas can be used to simplify trigonometric expressions, solve equations, and prove identities. What is Required Formulae involving multiple and sub-multiple angles Here are some of the commonly used required trigonometric formulas involving multiple and sub-multiple angles: These formulas can…
Trigonometry addition and subtraction formulas are used to find the trigonometric functions of the sum or difference of two angles. There are several formulas for each of the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. Here are the trigonometry addition and subtraction formulas: sin(A+B) = sin(A)cos(B) + cos(A)sin(B) sin(A-B) = sin(A)cos(B) –…
Trigonometric functions are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The most commonly used trigonometric functions are sine (sin), cosine (cos), and tangent (tan). These functions can be defined in terms of the sides of a right triangle as follows: In addition to these three functions,…
