# Tan 55 Degrees — Value of tan(55°) and How to Find It

TL;DR

The value of tan 55 degrees is approximately 1.4281 — it is not a special-angle exact value, so there is no clean surd for it. This article shows how to find tan⁡55° honestly (calculator, the cofunction cot⁡35°, and table interpolation), gives the radian form, and explains why the value is greater than 1.

The value of **tan 55 degrees** is approximately 1.4281 (1.42814801 to eight places). Unlike tan⁡45° or tan⁡60°, the angle 55° is not a special angle, so tan⁡55° has no simple exact surd — it is read from a calculator, a trig table, or rewritten as the cofunction cot⁡35°.

> **Quick Answer:**
>
> **Result:** tan⁡55°≈1.4281
> **In radians:** tan⁡(11π/36)=tan(0.95993)≈1.4281
> **Notation:** decimal approximation — 1.42814801 (8 dp)
> **Method shown:** calculator (degree mode), the cofunction identity tan⁡55°=cot⁡35°, and table interpolation
> **Exact form:** none simple — 55° is not a special angle, so no clean radical exists

## What Does Tan 55 Degrees Mean?

Tangent of an angle is the ratio of sine to cosine: tan⁡θ=sin⁡θ/cos⁡θ. On the [unit circle](/content/math/geometry/unit-circle/index.html), that is the y-coordinate divided by the x-coordinate of the point at angle θ.

A **quadrant** is one of the four regions the axes divide the plane into, numbered anticlockwise from the top right; 55° lands in Quadrant I, where sine and cosine are both positive, so tangent is positive too.

Because 55° is past 45° (where sin⁡=cos), the numerator now exceeds the denominator, so tan⁡55°>1. That ratio works out to about 1.4281.

## How Do You Find the Value of Tan 55 Degrees?

Because 55° is not a special angle, there is no surd to simplify to. **So how do you find tan 55 degrees without a calculator?** You rewrite it as a cofunction or interpolate from a table — here are the three honest routes.

### Method 1: Calculator (set to degree mode)

Type tan⁡(55) with the calculator in **DEG** mode.

tan⁡55°=1.42814801…≈1.4281

In radian mode the same keystrokes give tan⁡(55 rad)≈−6.40 — a completely different number, so the mode matters.

### Method 2: Cofunction identity

Tangent and cotangent are [cofunctions](/content/math/trigonometry/cofunction-identities/index.html): tan⁡θ=cot⁡(90°−θ).

tan⁡55°=cot⁡(90°−55°)=cot⁡35°=
\frac{1}{tan⁡35°}.

Since tan⁡35°≈0.7002, this gives \frac{1}{0.7002}≈1.4281 — the same value, confirmed a second way.

### Method 3: Table interpolation

If a trig table lists tan⁡54°=1.3764 and tan⁡56°=1.4826, estimate tan⁡55° by linear interpolation:

tan⁡55°≈1.3764+\frac{55−54}{56−54}(1.4826−1.3764)=1.3764+0.5(0.1062)=1.4295.

That lands within 0.001 of the true 1.4281. Interpolation carries a slightly larger error for tangent than for sine.

### What is tan 55 degrees in radians?

The angle converts to 11π/36≈0.9599, but the _value_ of the tangent is the same number, ≈1.4281. Converting the angle does not change the tangent.

## Examples Using Tan 55 Degrees

### Example 1

**State tan⁡55° to four decimal places.**

From a calculator in degree mode, tan⁡55°=1.4281.

### Example 2 (wrong path first)

**Find tan⁡55° from sin⁡55° and cos⁡55°.**

_Wrong attempt._ A student writes tan⁡55°=sin⁡55°×cos⁡55°=0.8192×0.5736=0.4698.

_Why it breaks._ Tangent is sine **divided by** cosine, not multiplied: tan⁡θ=\frac{sin⁡θ}{cos⁡θ}. Multiplying gives a number below 1, which can't be right for an angle past 45°.

_Correct._ tan⁡55°=\frac{sin⁡55°}{cos⁡55°}=\frac{0.8192}{0.5736}=1.4281.

### Example 3

**A road climbs at 55° to the horizontal. How many metres does it rise over a 20 m horizontal run?**

Rise =20×tan⁡55°=20×1.4281=28.56 m.

### Example 4

**Compare tan⁡55° with tan⁡45°.**

tan⁡45°=1; tan⁡55°=1.4281. The extra 10° raises the value by 0.43 — far more than the same 10° would change a sine.

### Example 5

**Verify tan⁡55°=cot⁡35° on a calculator.**

tan⁡55°=1.42815 and cot⁡35°=\frac{1}{tan⁡35°}=1.42815 — identical, confirming the cofunction identity.

## Tan 55 Degrees — Tripping Points to Avoid

Most errors on a non-special tangent come from a few repeatable habits.

### Mistake 1: Multiplying sine and cosine instead of dividing

**Where it slips in:** building tangent from sin⁡θ and cos⁡θ.

**Don't do this:** writing tan⁡55°=sin⁡55°×cos⁡55°.

**The correct way:** tangent is the quotient \frac{sin⁡θ}{cos⁡θ}. The habit that fixes this is to read "tangent" as "sine over cosine" before writing anything.

### Mistake 2: Using the wrong cofunction

**Where it slips in:** rewriting tan⁡55° as a complementary angle.

**Don't do this:** writing tan⁡55°=tan⁡35°.

**The correct way:** the complement of tangent is cotangent — tan⁡55°=cot⁡35°, which equals \frac{1}{tan⁡35°}, not tan⁡35° itself.

### Mistake 3: Forgetting the calculator's angle mode

**Where it slips in:** the calculator was left in radian mode.

**Don't do this:** reading tan⁡(55)=−6.40 and reporting it as tan⁡55°.

**The correct way:** check **DEG** mode for tan⁡55°; −6.40 is tan⁡(55 radians).

## Key Takeaways

- **Tan 55 degrees** is approximately 1.4281 — a decimal, not a clean surd.
- 55° is not a special angle, so the value comes from a calculator, the cofunction cot⁡35°, or interpolation.
- tan⁡55°>1 because 55° is past the 45° point where sine and cosine are equal.
- In radians the angle is 11π/36, but the tangent value stays ≈1.4281.
- The biggest slip is multiplying sine and cosine instead of dividing.