Tan 5 Degrees
The value of tan 5 degrees is 0.0874886. . .. Tan 5 degrees in radians is written as tan (5° × π/180°), i.e., tan (π/36) or tan (0.087266. . .). In this article, we will discuss the methods to find the value of tan 5 degrees with examples.
 Tan 5° in decimal: 0.0874886. . .
 Tan (5 degrees): 0.0874886. . .
 Tan 5° in radians: tan (π/36) or tan (0.0872664 . . .)
What is the Value of Tan 5 Degrees?
The value of tan 5 degrees in decimal is 0.087488663. . .. Tan 5 degrees can also be expressed using the equivalent of the given angle (5 degrees) in radians (0.08726 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 5 degrees = 5° × (π/180°) rad = π/36 or 0.0872 . . .
∴ tan 5° = tan(0.0872) = 0.0874886. . .
Explanation:
For tan 5 degrees, the angle 5° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 5° value = 0.0874886. . .
Since the tangent function is a periodic function, we can represent tan 5° as, tan 5 degrees = tan(5° + n × 180°), n ∈ Z.
⇒ tan 5° = tan 185° = tan 365°, and so on.
Note: Since, tangent is an odd function, the value of tan(5°) = tan(5°).
Methods to Find Value of Tan 5 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 5° is given as 0.08748. . .. We can find the value of tan 5 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Tan 5 Degrees Using Unit Circle
To find the value of tan 5 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 5° angle with the positive xaxis.
 The tan of 5 degrees equals the ycoordinate(0.0872) divided by xcoordinate(0.9962) of the point of intersection (0.9962, 0.0872) of unit circle and r.
Hence the value of tan 5° = y/x = 0.0875 (approx).
Tan 5° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 5 degrees as:
 sin(5°)/cos(5°)
 ± sin 5°/√(1  sin²(5°))
 ± √(1  cos²(5°))/cos 5°
 ± 1/√(cosec²(5°)  1)
 ± √(sec²(5°)  1)
 1/cot 5°
Note: Since 5° lies in the 1st Quadrant, the final value of tan 5° will be positive.
We can use trigonometric identities to represent tan 5° as,
 cot(90°  5°) = cot 85°
 cot(90° + 5°) = cot 95°
 tan (180°  5°) = tan 175°
☛ Also Check:
Examples Using Tan 5 Degrees

Example 1: Find the value of 2 tan(5°)/5 tan(175°).
Solution:
Using trigonometric identities, we know, tan(5°) = tan(180°  5°) = tan 175°.
⇒ tan(5°) = tan(175°)
⇒ Value of 2 tan(5°)/5 tan(175°) = 2/5 
Example 2: Find the value of (2 sin (2.5°) cos (2.5°) sec (5°)). [Hint: Use tan 5° = 0.0875]
Solution:
Using sin 2a formula,
2 sin (2.5°) cos (2.5°) = sin (2 × 2.5°) = sin 5°
⇒ 2 sin (2.5°) cos (2.5°) sec(5°) = sin 5° sec 5°
= sin 5°/cos 5° = tan 5°
⇒ (2 sin (2.5°) cos (2.5°) sec(5°)) = 0.0875 
Example 3: Using the value of tan 5°, solve: (sec²(5°)  1).
Solution:
We know, (sec²(5°)  1) = (tan²(5°)) = 0.0077
⇒ (sec²(5°)  1) = 0.0077
FAQs on Tan 5 Degrees
What is Tan 5 Degrees?
Tan 5 degrees is the value of tangent trigonometric function for an angle equal to 5 degrees. The value of tan 5° is 0.0875 (approx).
What is the Value of Tan 5 Degrees in Terms of Cot 5°?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 5° as 1/cot(5°). The value of cot 5° is equal to 11.43005.
What is the Value of Tan 5° in Terms of Cosec 5°?
Since the tangent function can be represented using the cosecant function, we can write tan 5° as 1/√(cosec²(5°)  1). The value of cosec 5° is equal to 11.47371.
How to Find the Value of Tan 5 Degrees?
The value of tan 5 degrees can be calculated by constructing an angle of 5° with the xaxis, and then finding the coordinates of the corresponding point (0.9962, 0.0872) on the unit circle. The value of tan 5° is equal to the ycoordinate(0.0872) divided by the xcoordinate (0.9962). ∴ tan 5° = 0.0875
How to Find Tan 5° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 5° can be given in terms of other trigonometric functions as:
 sin(5°)/cos(5°)
 ± sin 5°/√(1  sin²(5°))
 ± √(1  cos²(5°))/cos 5°
 ± 1/√(cosec²(5°)  1)
 ± √(sec²(5°)  1)
 1/cot 5°
☛ Also check: trigonometric table
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