Understanding the Tangent of an Angle in Trigonometry | Calculation and Explanation with an Example

tan 45°

The tangent of an angle is a trigonometric function that relates the ratio of the length of the opposite side to the length of the adjacent side of a right triangle

The tangent of an angle is a trigonometric function that relates the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.

To calculate the tangent of 45°, we need to form a right triangle and determine the ratios of the sides.

In a right triangle, two sides are perpendicular to each other, forming a 90° angle. We know that a 45° angle is formed when these two sides are equal in length.

Let’s assume that the length of each side is 1 unit. We can label the sides as follows:
– The side opposite to the 45° angle is called the “opposite” side.
– The side adjacent to the 45° angle is called the “adjacent” side.

In this case, the opposite side and adjacent side both have lengths of 1 unit.

Now, to find the tangent of 45°, we calculate the ratio:

tan(45°) = opposite/adjacent
= 1/1
= 1

Therefore, the tangent of 45° is 1.

As a tutor, I would also make sure to explain that the tangent function can be used with any angle measure, not just 45°. The result of the tangent function varies depending on the angle being used.

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