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 x-axis.
• The tan of 3 degrees equals the y-coordinate(0.0523) divided by x-coordinate(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:

• tan 40 degrees
• tan 3 degrees
• tan 690 degrees
• tan 23 degrees
• tan 36 degrees
• tan 110 degrees

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 x-axis, 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 y-coordinate(0.0523) divided by the x-coordinate (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