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Tan 26 Degrees

The value of tan 26 degrees is 0.4877325. . .. Tan 26 degrees in radians is written as tan (26° × π/180°), i.e., tan (13π/90) or tan (0.453785. . .). In this article, we will discuss the methods to find the value of tan 26 degrees with examples.

Tan 26° in decimal: 0.4877325. . .
Tan (-26 degrees): -0.4877325. . .
Tan 26° in radians: tan (13π/90) or tan (0.4537856 . . .)

What is the Value of Tan 26 Degrees?

The value of tan 26 degrees in decimal is 0.487732588. . .. Tan 26 degrees can also be expressed using the equivalent of the given angle (26 degrees) in radians (0.45378 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 26 degrees = 26° × (π/180°) rad = 13π/90 or 0.4537 . . .
∴ tan 26° = tan(0.4537) = 0.4877325. . .

Explanation:

For tan 26 degrees, the angle 26° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 26° value = 0.4877325. . .
Since the tangent function is a periodic function, we can represent tan 26° as, tan 26 degrees = tan(26° + n × 180°), n ∈ Z.
⇒ tan 26° = tan 206° = tan 386°, and so on.
Note: Since, tangent is an odd function, the value of tan(-26°) = -tan(26°).

Methods to Find Value of Tan 26 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 26° is given as 0.48773. . .. We can find the value of tan 26 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 26° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 26 degrees as:

sin(26°)/cos(26°)
± sin 26°/√(1 - sin²(26°))
± √(1 - cos²(26°))/cos 26°
± 1/√(cosec²(26°) - 1)
± √(sec²(26°) - 1)
1/cot 26°

Note: Since 26° lies in the 1st Quadrant, the final value of tan 26° will be positive.

We can use trigonometric identities to represent tan 26° as,

cot(90° - 26°) = cot 64°
-cot(90° + 26°) = -cot 116°
-tan (180° - 26°) = -tan 154°

Tan 26 Degrees Using Unit Circle

To find the value of tan 26 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 26° angle with the positive x-axis.
The tan of 26 degrees equals the y-coordinate(0.4384) divided by x-coordinate(0.8988) of the point of intersection (0.8988, 0.4384) of unit circle and r.

Hence the value of tan 26° = y/x = 0.4877 (approx).

☛ Also Check:

Examples Using Tan 26 Degrees

Example 1: Find the value of 2 tan 13°/(1 - tan²(13°)). [Hint: Use tan 26° = 0.4877]

Solution:

Using the tan 2a formula,
2 tan 13°/(1 - tan²(13°)) = tan(2 × 13°) = tan 26°
∵ tan 26° = 0.4877
⇒ 2 tan 13°/(1 - tan²(13°)) = 0.4877
Example 2: Find the value of tan 26° if cot 26° is 2.0503.

Solution:
Since, tan 26° = 1/cot 26°
⇒ tan 26° = 1/2.0503 = 0.4877
Example 3: Find the value of 2 tan(26°)/8 tan(154°).

Solution:

Using trigonometric identities, we know, tan(26°) = -tan(180° - 26°) = -tan 154°.
⇒ tan(26°) = -tan(154°)
⇒ Value of 2 tan(26°)/8 tan(154°) = -2/8 = -1/4

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FAQs on Tan 26 Degrees

What is Tan 26 Degrees?

Tan 26 degrees is the value of tangent trigonometric function for an angle equal to 26 degrees. The value of tan 26° is 0.4877 (approx).

What is the Value of Tan 26 Degrees in Terms of Cot 26°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 26° as 1/cot(26°). The value of cot 26° is equal to 2.05030.

How to Find the Value of Tan 26 Degrees?

The value of tan 26 degrees can be calculated by constructing an angle of 26° with the x-axis, and then finding the coordinates of the corresponding point (0.8988, 0.4384) on the unit circle. The value of tan 26° is equal to the y-coordinate(0.4384) divided by the x-coordinate (0.8988). ∴ tan 26° = 0.4877

What is the Exact Value of tan 26 Degrees?

The exact value of tan 26 degrees can be given accurately up to 8 decimal places as 0.48773258.

How to Find Tan 26° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 26° can be given in terms of other trigonometric functions as:

sin(26°)/cos(26°)
± sin 26°/√(1 - sin²(26°))
± √(1 - cos²(26°))/cos 26°
± 1/√(cosec²(26°) - 1)
± √(sec²(26°) - 1)
1/cot 26°

☛ Also check: trigonometric table

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