Tangent θ (tan θ)
In mathematics, the tangent of an angle θ, denoted as tan θ, is a trigonometric function that relates the ratio of the length of the side opposite to the angle θ to the length of the side adjacent to the angle θ in a right triangle
In mathematics, the tangent of an angle θ, denoted as tan θ, is a trigonometric function that relates the ratio of the length of the side opposite to the angle θ to the length of the side adjacent to the angle θ in a right triangle.
To understand the concept of tangent, consider a right triangle where one of the angles is θ. The side opposite to the angle θ is referred to as the “opposite” side, and the side adjacent to the angle θ is referred to as the “adjacent” side.
The tangent of θ is then defined as the ratio of the length of the opposite side to the length of the adjacent side:
tan θ = opposite / adjacent
For example, if we have a right triangle with an angle θ and the opposite side has a length of 5 units, while the adjacent side has a length of 3 units, the tangent of θ would be:
tan θ = 5 / 3
It is important to note that the tangent function is applicable only to right triangles, but its concept can be extended to any angle in the context of trigonometry.
The tangent function is periodic, meaning it repeats itself after a certain interval. This interval is π radians (180 degrees). As θ increases, the values of tan θ will keep changing, oscillating between positive and negative infinity.
The tangent function has many applications in various fields such as physics, engineering, and computer graphics, where it is commonly used to model and analyze various periodic phenomena.
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