tan(45°) = 1

The tangent of 45 degrees is 1.

Calculation Result

tan(45°) = 1

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The tangent function (tan) is one of the fundamental trigonometric functions that relates an angle to the ratio of two sides in a right triangle. This calculator computes the tangent of any angle in degrees, providing instant and accurate results for mathematical, scientific, and engineering applications. Note that tangent is undefined at 90° and 270° due to division by zero.

Enter any angle in degrees (e.g., 30, 45, 60). Note: tan(90°) and tan(270°) are undefined.

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Mathematical Explanation

The tangent function is defined as tan(θ) = opposite/adjacent in a right triangle, or equivalently as tan(θ) = sin(θ)/cos(θ). For a unit circle, tangent represents the slope of the line from the origin through a point on the circle at a given angle. The tangent function is periodic with period 180° (or π radians) and has vertical asymptotes where cosine equals zero.

Frequently Asked Questions

The tangent function (tan) is a trigonometric function that calculates the ratio of the opposite side to the adjacent side in a right triangle. It's one of the three primary trigonometric functions along with sine and cosine.

tan(45°) equals 1 exactly. This occurs because at 45 degrees, the opposite and adjacent sides of a right triangle are equal in length.

tan(90°) is undefined because tangent equals sin(θ)/cos(θ), and cos(90°) equals zero, resulting in division by zero. The tangent function approaches positive or negative infinity as it nears 90 degrees.

Yes, unlike sine and cosine, the tangent function can have any real value from negative infinity to positive infinity. It exceeds 1 for angles between 45° and 90° (and equivalent angles in other quadrants).

This calculator uses degrees as input. If you have an angle in radians, multiply it by 180/π to convert to degrees before using this calculator.

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