Tangent Calculator

In a right-angled triangle, the tangent of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to it. Mathematically, this is expressed as tan(angle) = Opposite / Adjacent. Alternatively, tangent can be computed using sine and cosine values through the identity tan(angle) = sin(angle) / cos(angle). When using this calculator, angles provided in degrees are internally converted to radians using the formula radians = degrees * (π / 180) before executing the trigonometric computation.

Let us walk through finding the tangent of a 45-degree angle. First, convert the angle from degrees to radians: 45 * (π / 180) = π / 4 radians (approximately 0.7854). Next, apply the tangent formula: tan(0.7854). Because the sine and cosine of 45 degrees are both equal to √2 / 2, their quotient evaluates precisely to 1. Thus, the tangent of a 45-degree angle is 1, which means the opposite and adjacent sides of the corresponding right triangle are equal in length.

Always verify whether your input angle is measured in degrees or radians before calculating, as confusing the two will lead to incorrect outputs. Keep in mind that the tangent function is undefined at odd multiples of 90 degrees (such as 90°, 270°), where the cosine evaluates to zero, resulting in a vertical asymptote. When applying tangent to real-world physics or construction problems, double-check your unit consistency to ensure your final ratios translate correctly into physical dimensions.