Calculate Tangent & Inverse Tangent
This free online calculator helps you compute tangent (tan) and inverse tangent (tan⁻¹) values in degrees and radians.
Tangent Calculator (tan(θ))
Result:
Inverse Tangent Calculator (tan⁻¹(x))
Degrees (°):
Radians (rad):
Tangent Table
| Degrees | Tangent Value |
|---|---|
| 0° | 0 |
| 30° | 1/√3 |
| 45° | 1 |
| 60° | √3 |
| 90° | ∞ (Infinity) |
| 180° | 0 |
| 270° | ∞ (Infinity) |
| 360° | 0 |
Interactive Tangent Graph
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How It Works
**Tangent (tan):** In a right-angled triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. This can also be expressed in terms of sine and cosine:
tan(θ) = sin(θ) / cos(θ)
**Inverse Tangent (tan⁻¹):** Also known as arctangent, this function does the reverse. It takes the ratio of the sides and calculates the corresponding angle.
θ = tan⁻¹(x)
**Periodicity:** The tangent function is periodic with a period of 180° or π radians. This means the values repeat every 180°. For example, tan(45°) = tan(225°) = 1.
Frequently Asked Questions (FAQs)
What is the value of tan(90°)?
The tangent of 90° (and 270°) is infinity (∞). This is because tan(θ) = sin(θ)/cos(θ), and at these angles, cos(θ) approaches zero, causing the value to go to infinity.
Why does tangent have a period of 180°?
The tangent function has a period of 180° because the signs of both sine and cosine change every 180° but the ratio remains the same. For example, sin(45°) = 1/√2 and cos(45°) = 1/√2, so tan(45°) = 1. At 225° (45° + 180°), sin(225°) = -1/√2 and cos(225°) = -1/√2, so the ratio tan(225°) = 1 is the same.
Is inverse tangent the same as cotangent?
No, they are different functions. Inverse tangent (tan⁻¹(x) or arctan) finds the angle whose tangent is x. The cotangent (cot(θ)) is the reciprocal of the tangent function, meaning cot(θ) = 1/tan(θ).