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Tan 55 Degrees

The value of tan 55 degrees is 1.4281480. . .. Tan 55 degrees in radians is written as tan (55° × π/180°), i.e., tan (11π/36) or tan (0.959931. . .). In this article, we will discuss the methods to find the value of tan 55 degrees with examples.

Tan 55° in decimal: 1.4281480. . .
Tan (-55 degrees): -1.4281480. . .
Tan 55° in radians: tan (11π/36) or tan (0.9599310 . . .)

What is the Value of Tan 55 Degrees?

The value of tan 55 degrees in decimal is 1.428148006. . .. Tan 55 degrees can also be expressed using the equivalent of the given angle (55 degrees) in radians (0.95993 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 55 degrees = 55° × (π/180°) rad = 11π/36 or 0.9599 . . .
∴ tan 55° = tan(0.9599) = 1.4281480. . .

Explanation:

For tan 55 degrees, the angle 55° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 55° value = 1.4281480. . .
Since the tangent function is a periodic function, we can represent tan 55° as, tan 55 degrees = tan(55° + n × 180°), n ∈ Z.
⇒ tan 55° = tan 235° = tan 415°, and so on.
Note: Since, tangent is an odd function, the value of tan(-55°) = -tan(55°).

Methods to Find Value of Tan 55 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 55° is given as 1.42814. . .. We can find the value of tan 55 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 55° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 55 degrees as:

sin(55°)/cos(55°)
± sin 55°/√(1 - sin²(55°))
± √(1 - cos²(55°))/cos 55°
± 1/√(cosec²(55°) - 1)
± √(sec²(55°) - 1)
1/cot 55°

Note: Since 55° lies in the 1st Quadrant, the final value of tan 55° will be positive.

We can use trigonometric identities to represent tan 55° as,

cot(90° - 55°) = cot 35°
-cot(90° + 55°) = -cot 145°
-tan (180° - 55°) = -tan 125°

Tan 55 Degrees Using Unit Circle

To find the value of tan 55 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 55° angle with the positive x-axis.
The tan of 55 degrees equals the y-coordinate(0.8192) divided by x-coordinate(0.5736) of the point of intersection (0.5736, 0.8192) of unit circle and r.

Hence the value of tan 55° = y/x = 1.4281 (approx).

☛ Also Check:

Examples Using Tan 55 Degrees

Example 1: Find the value of 2 tan 27.5°/(1 - tan²(27.5°)). [Hint: Use tan 55° = 1.4281]

Solution:

Using the tan 2a formula,
2 tan 27.5°/(1 - tan²(27.5°)) = tan(2 × 27.5°) = tan 55°
∵ tan 55° = 1.4281
⇒ 2 tan 27.5°/(1 - tan²(27.5°)) = 1.4281
Example 2: Find the value of 5 tan(55°)/9 tan(125°).

Solution:

Using trigonometric identities, we know, tan(55°) = -tan(180° - 55°) = -tan 125°.
⇒ tan(55°) = -tan(125°)
⇒ Value of 5 tan(55°)/9 tan(125°) = -5/9
Example 3: Simplify: 9 (tan 55°/cot 35°)

Solution:

We know tan 55° = cot 35°
⇒ 9 tan 55°/cot 35° = 9 (tan 55°/tan 55°)
= 9(1) = 9

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FAQs on Tan 55 Degrees

What is Tan 55 Degrees?

Tan 55 degrees is the value of tangent trigonometric function for an angle equal to 55 degrees. The value of tan 55° is 1.4281 (approx).

What is the Exact Value of tan 55 Degrees?

The exact value of tan 55 degrees can be given accurately up to 8 decimal places as 1.42814800.

What is the Value of Tan 55 Degrees in Terms of Sin 55°?

Using trigonometric identities, we can write tan 55° in terms of sin 55° as, tan(55°) = sin 55°/√(1 - sin²(55°)) . Here, the value of sin 55° is equal to 0.8192.

How to Find Tan 55° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 55° can be given in terms of other trigonometric functions as:

sin(55°)/cos(55°)
± sin 55°/√(1 - sin²(55°))
± √(1 - cos²(55°))/cos 55°
± 1/√(cosec²(55°) - 1)
± √(sec²(55°) - 1)
1/cot 55°

☛ Also check: trigonometric table

How to Find the Value of Tan 55 Degrees?

The value of tan 55 degrees can be calculated by constructing an angle of 55° with the x-axis, and then finding the coordinates of the corresponding point (0.5736, 0.8192) on the unit circle. The value of tan 55° is equal to the y-coordinate(0.8192) divided by the x-coordinate (0.5736). ∴ tan 55° = 1.4281

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