The tangent of an angle is defined in terms of that angle being one of the angles of a right triangle.  In a right triangle the tangent is the ratio of side opposite the angle to the side adjacent to the angle.  See the graphic representing the right triangle. 

The Tangent function has a vertical asymptote at every (n + 1/2) * `pi` radians; i.e. at ...,-450 degrees, -270 degrees, -90 degrees, 90 degrees, 270 degrees, 450 degrees, ....

Notes

Here's a graphical depiction of the tangent kind of drawn on it's side.  As the

Scientific Calculator Functions

Basic Math Functions:

• x^-1: This is the mathematical inverse or reciprocal of x, which is also 1/x
• x! : This is the factorial of x
• x²: This is the square of x
• x³: This is the cube of x
• x^y: This is x to the y^th power
• 10^x: This is ten to the x^th power.
• `sqrt(x)`: This is the square root of x
• `root(3)(x)`: This is the cube root of x
• `root(y)(x)`: This is the y^th root of x
• Rand: This returns a random number between 0 and 1.
• log(x): This the base 10 log of x
• ln(x) : This provides the natural log of x
• MOD: This provides the integer remainder of x/y.
• GCD: This is the greatest common divisor of two numbers

Math Constants:

• e - this is the base of the natural log
• π - This is the base of Euclidean geometry

Trigonometry Functions:

• sin(θ) : This is the sine function of an angle.
• cos(θ): This is the cosine function of an angle.
• tan(θ): This is the tangent function of an angle.
• sin^-1(x): This is the angle from the inverse of a sine.
• cos^-1(x): This is the angle from the inverse of a cosine.
• tan^-1(x): This is the angle from the inverse of a tangent.

Unit Conversions:

• Length: This converts an input length to compatible units.
• Area: This converts an input area to compatible units.
• Volume: This converts an input volume to compatible units.
• Velocity: This converts an input velocity to compatible units.
• Mass: This converts an input mass or weight to compatible units.
• Temp: This converts and input temperature to compatible units.
• Force: This converts an input force to compatible units.
• Pressure: This converts an input pressure to compatible units.

Other Math / Science Calculators:

• 3D Vector Calculator
• Quaternion Calculator
• Statistics Calculator