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

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: $\tan 55° \approx 1.4281$

In radians: $\tan\left(\frac{11\pi}{36}\right) = \tan(0.95993) \approx 1.4281$

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: $\tan\theta = \dfrac{\sin\theta}{\cos\theta}$. On the unit circle, that is the $y$-coordinate divided by the $x$-coordinate of the point at angle $\theta$.

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 $\sin = \cos$ and the ratio is exactly $1$), 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.

$$\tan 55° = 1.42814801\ldots \approx 1.4281$$

In radian mode the same keystrokes give $\tan(55\ \text{rad}) \approx -6.40$ — a completely different number, so the mode matters.

Method 2: Cofunction identity

Tangent and cotangent are cofunctions: $\tan\theta = \cot(90° - \theta)$.

$$\tan 55° = \cot(90° - 55°) = \cot 35° = \frac{1}{\tan 35°}$$

Since $\tan 35° \approx 0.7002$, this gives $\dfrac{1}{0.7002} \approx 1.4281$ — 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:

$$\tan 55° \approx 1.3764 + \frac{55 - 54}{56 - 54},(1.4826 - 1.3764) = 1.3764 + 0.5(0.1062) = 1.4295$$

That lands within $0.0014$ of the true $1.4281$. Interpolation carries a slightly larger error for tangent than for sine, because the tangent curve bends more sharply as the angle grows.

What is tan 55 degrees in radians?

The angle converts to $\frac{11\pi}{36} \approx 0.9599$ rad, but the value of the tangent is the same number, $\approx 1.4281$. Converting the angle does not change the tangent; it only relabels the angle.

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 $\tan 55° = \sin 55° \times \cos 55° = 0.8192 \times 0.5736 = 0.4698$.

Why it breaks. Tangent is sine divided by cosine, not multiplied: $\tan\theta = \tfrac{\sin\theta}{\cos\theta}$. Multiplying gives a number below $1$, which can't be right for an angle past $45°$.

Correct. $\tan 55° = \dfrac{\sin 55°}{\cos 55°} = \dfrac{0.8192}{0.5736} = 1.4281$.

Example 3

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

Rise $= 20 \times \tan 55° = 20 \times 1.4281 = 28.56$ 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, because tangent accelerates near the steep end.

Example 5

Verify $\tan 55° = \cot 35°$ on a calculator.

$\tan 55° = 1.42815$ and $\cot 35° = \tfrac{1}{\tan 35°} = 1.42815$ — 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 $\sin\theta$ and $\cos\theta$.

Don't do this: writing $\tan 55° = \sin 55° \times \cos 55°$.

The correct way: tangent is the quotient $\tfrac{\sin\theta}{\cos\theta}$. The habit that fixes this is to read "tangent" as "sine over cosine" out loud before writing anything; the learner who reaches for multiplication will get a value below $1$ for an angle that must exceed $1$.

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 $\tfrac{1}{\tan 35°}$, 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 $\tan(55\ \text{radians})$, an angle of more than eight full turns, where tangent can even be negative.

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 $\frac{11\pi}{36}$, but the tangent value stays $\approx 1.4281$.

• The biggest slip is multiplying sine and cosine instead of dividing.

To take tangent values further with a teacher, explore Bhanzu's trigonometry tutor, a high school math tutor, or math tutoring.

Practice These Before Moving On

1. State $\tan 55°$ to four decimal places.

2. Rewrite $\tan 55°$ as a cotangent and check it equals $\tfrac{1}{\tan 35°}$.

3. Use $\tan 54° = 1.3764$ and $\tan 56° = 1.4826$ to interpolate $\tan 55°$.

Want a live trainer to walk through more tangent-value problems? Book a free demo class.

Read More

• Sin Cos Tan — the three core trigonometric ratios

• Trigonometric Ratios — definition, formulas, and examples

• Reciprocal Identities — secant, cosecant, and cotangent

• Angle of Depression — sightlines below the horizontal

• Trigonometric Table — ratios for standard angles