Tangent compares sine to cosine and also equals opposite over adjacent in a right triangle. It can be any real value and becomes undefined where cosine is zero.
⚠Tangent is undefined at angles where cosine equals zero. The calculator shows an error message for those boundary cases.
How Tangent Works
Tangent describes steepness and slope. On a graph, it repeats every 180 degrees or π radians and has vertical asymptotes.
Right Triangle
tan(θ)=opposite/adjacent.
Identity
tan(θ)=sin(θ)/cos(θ).
Undefined Cases
Undefined when cos(θ)=0.
Period
Tangent repeats every 180° or π.
💡 Example: For 45°, tan(45°)=1.
Applications of Tangent
SlopeSurveyingElevation AnglesNavigation
Frequently Asked Questions
What is a tangent calculator?▼
It calculates tan(x) for an angle entered in degrees or radians.
What is the tangent formula?▼
tan(θ)=opposite/adjacent in a right triangle, and tan(θ)=sin(θ)/cos(θ).
How do I use this calculator?▼
Enter an angle, choose degrees or radians, and click Calculate.
When is tangent undefined?▼
Tangent is undefined when cos(θ)=0, such as 90° and 270°.
Where is tangent used?▼
Tangent is used for slopes, angles of elevation, surveying, navigation, and right triangle problems.
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