Tangent facts for kids

The word tangent can mean a couple of different things, especially in math! It can describe a special line that just touches a curve, or it can be a type of math function used with angles.

What is a Tangent Line in Geometry?

In geometry, a tangent is a straight line that touches a curve or a circle at only one single point. Imagine a bicycle wheel rolling along the ground. The ground itself is tangent to the wheel at the exact spot where the wheel touches it. The line doesn't cross through the curve or circle. It just "kisses" it at that one spot.

Tangents and Circles

For a circle, a tangent line always forms a right angle (90 degrees) with the radius of the circle at the point where it touches. This point is called the point of tangency.

Tangents and Curves

When we talk about more complex curves, a tangent line shows the direction the curve is going at that specific point. It's like looking at a road; the tangent line tells you which way the road is heading right at that moment. This idea is very important in calculus, a higher level of math.

What is Tangent in Trigonometry?

The word tangent also refers to a special trigonometric function. Trigonometry is a branch of math that studies the relationships between the sides and angles of triangles.

Tangent in Right-Angled Triangles

In a right-angled triangle (a triangle with one 90-degree angle), the tangent of an angle is found by dividing the length of the side opposite the angle by the length of the side adjacent (next to) the angle.

• Opposite side: The side across from the angle you are looking at.
• Adjacent side: The side next to the angle, but not the longest side (hypotenuse).

We often write this as: tangent (angle) = opposite / adjacent

Using the Tangent Function

The tangent function is used to solve problems involving angles and distances. For example, if you know the angle of elevation to the top of a tree and how far you are standing from its base, you can use the tangent function to figure out the tree's height.

Images for kids

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  At each point, the moving line is always tangent to the curve. Its slope is the derivative; green marks positive derivative, red marks negative derivative and black marks zero derivative. The point (x,y) = (0,1) where the tangent intersects the curve, is not a max, or a min, but is a point of inflection.

See also

In Spanish: Tangente (geometría) para niños