Exact
1
Tan 45 Degrees
Answer
tan 45° equals 1, which is approximately 1.
Decimal
1
Formula
tan 45° = sin 45° / cos 45° = 1 ≈ 1
Worked steps
1
From sin and cos
tan(angle) = sin(angle) / cos(angle). tan 45° = (√2/2) / (√2/2) = 1.
2
Calculator method (DEG mode)
Set the calculator to DEG. Press tan, type 45, press =. Result: 1.
3
Inverse check
To go back from a tangent value to the angle, use tan⁻¹ (or arctan). On the calculator in DEG mode, tan⁻¹(1) returns 45°.
About this value
Tan 45° = 1 is one of the standard tangent values memorised in trigonometry. At 45° the opposite and adjacent sides are equal, so tan = 1. This is the only standard angle where tan equals exactly one.
Frequently asked questions
What is tan 45 degrees?
Tan 45 Degrees equals 1 as an exact value, or 1 as a decimal. The exact form is what you'd typically write in exam working; the decimal is what your calculator displays.
How do I enter this on a calculator?
Set the angle mode to DEG. Press tan, type the angle, press =. If your calculator is in RAD mode by mistake, you will get a different answer — always check the mode pill before pressing a trig function.
Why memorise the standard angle values?
The values for 30°, 45°, 60°, and 90° appear in almost every trigonometry problem at school level. Knowing the exact form (with surds) lets you produce surd-form answers expected in exams, instead of decimal approximations.
What is this in radians?
To convert the angle to radians, multiply by π/180. The function value is the same regardless of mode — the answer for 45° is 1 in DEG or sin(angle_in_rad) of the equivalent radian measure.