Tan 3 Degrees
The value of tan 3 degrees is 0.0524077. . .. Tan 3 degrees in radians is written as tan (3° × π/180°), i.e., tan (π/60) or tan (0.052359. . .). In this article, we will discuss the methods to find the value of tan 3 degrees with examples.
 Tan 3° in decimal: 0.0524077. . .
 Tan (3 degrees): 0.0524077. . .
 Tan 3° in radians: tan (π/60) or tan (0.0523598 . . .)
What is the Value of Tan 3 Degrees?
The value of tan 3 degrees in decimal is 0.052407779. . .. Tan 3 degrees can also be expressed using the equivalent of the given angle (3 degrees) in radians (0.05235 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 3 degrees = 3° × (π/180°) rad = π/60 or 0.0523 . . .
∴ tan 3° = tan(0.0523) = 0.0524077. . .
Explanation:
For tan 3 degrees, the angle 3° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 3° value = 0.0524077. . .
Since the tangent function is a periodic function, we can represent tan 3° as, tan 3 degrees = tan(3° + n × 180°), n ∈ Z.
⇒ tan 3° = tan 183° = tan 363°, and so on.
Note: Since, tangent is an odd function, the value of tan(3°) = tan(3°).
Methods to Find Value of Tan 3 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 3° is given as 0.05240. . .. We can find the value of tan 3 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Tan 3 Degrees Using Unit Circle
To find the value of tan 3 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 3° angle with the positive xaxis.
 The tan of 3 degrees equals the ycoordinate(0.0523) divided by xcoordinate(0.9986) of the point of intersection (0.9986, 0.0523) of unit circle and r.
Hence the value of tan 3° = y/x = 0.0524 (approx).
Tan 3° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 3 degrees as:
 sin(3°)/cos(3°)
 ± sin 3°/√(1  sin²(3°))
 ± √(1  cos²(3°))/cos 3°
 ± 1/√(cosec²(3°)  1)
 ± √(sec²(3°)  1)
 1/cot 3°
Note: Since 3° lies in the 1st Quadrant, the final value of tan 3° will be positive.
We can use trigonometric identities to represent tan 3° as,
 cot(90°  3°) = cot 87°
 cot(90° + 3°) = cot 93°
 tan (180°  3°) = tan 177°
☛ Also Check:
Examples Using Tan 3 Degrees

Example 1: Find the value of 6 tan(3°)/10 tan(177°).
Solution:
Using trigonometric identities, we know, tan(3°) = tan(180°  3°) = tan 177°.
⇒ tan(3°) = tan(177°)
⇒ Value of 6 tan(3°)/10 tan(177°) = 6/10 = 3/5 
Example 2: Find the value of tan 3° if cot 3° is 19.0811.
Solution:
Since, tan 3° = 1/cot 3°
⇒ tan 3° = 1/19.0811 = 0.0524 
Example 3: Using the value of tan 3°, solve: (sec²(3°)  1).
Solution:
We know, (sec²(3°)  1) = (tan²(3°)) = 0.0027
⇒ (sec²(3°)  1) = 0.0027
FAQs on Tan 3 Degrees
What is Tan 3 Degrees?
Tan 3 degrees is the value of tangent trigonometric function for an angle equal to 3 degrees. The value of tan 3° is 0.0524 (approx).
How to Find the Value of Tan 3 Degrees?
The value of tan 3 degrees can be calculated by constructing an angle of 3° with the xaxis, and then finding the coordinates of the corresponding point (0.9986, 0.0523) on the unit circle. The value of tan 3° is equal to the ycoordinate(0.0523) divided by the xcoordinate (0.9986). ∴ tan 3° = 0.0524
What is the Value of Tan 3 Degrees in Terms of Cos 3°?
We know, using trig identities, we can write tan 3° as √(1  cos²(3°))/cos 3°. Here, the value of cos 3° is equal to 0.998629.
What is the Value of Tan 3° in Terms of Sec 3°?
We can represent the tangent function in terms of the secant function using trig identities, tan 3° can be written as √(sec²(3°)  1). Here, the value of sec 3° is equal to 1.0013.
How to Find Tan 3° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 3° can be given in terms of other trigonometric functions as:
 sin(3°)/cos(3°)
 ± sin 3°/√(1  sin²(3°))
 ± √(1  cos²(3°))/cos 3°
 ± 1/√(cosec²(3°)  1)
 ± √(sec²(3°)  1)
 1/cot 3°
☛ Also check: trigonometry table
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