Tan(45°) = 1
Tangent — sine divided by cosine, equivalently opposite/adjacent in a right triangle; undefined where cos = 0.
How to derive tan(45°)
In a 45-45-90 triangle the legs are equal, so opposite/adjacent = 1. Equivalently, tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1.
Unit-circle context
The angle 45° corresponds to π/4 radians and sits Quadrant I on the unit circle.
Other trig values at 45°
Related tan values
Frequently asked
- What is the exact value of tan(45°)?
- The exact value is 1. Its decimal approximation is 1.
- How do you derive tan(45°)?
- In a 45-45-90 triangle the legs are equal, so opposite/adjacent = 1. Equivalently, tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1.
- What is 45° in radians?
- 45° equals π/4 radians (multiply degrees by π/180).
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