Tan 28 Degrees

The value of tan 28 degrees is 0.5317094. . .. Tan 28 degrees in radians is written as tan (28° × π/180°), i.e., tan (7π/45) or tan (0.488692. . .). In this article, we will discuss the methods to find the value of tan 28 degrees with examples.

• Tan 28° in decimal: 0.5317094. . .
• Tan (-28 degrees): -0.5317094. . .
• Tan 28° in radians: tan (7π/45) or tan (0.4886921 . . .)

What is the Value of Tan 28 Degrees?

The value of tan 28 degrees in decimal is 0.531709431. . .. Tan 28 degrees can also be expressed using the equivalent of the given angle (28 degrees) in radians (0.48869 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 28 degrees = 28° × (π/180°) rad = 7π/45 or 0.4886 . . .
∴ tan 28° = tan(0.4886) = 0.5317094. . .

Explanation:

For tan 28 degrees, the angle 28° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 28° value = 0.5317094. . .
Since the tangent function is a periodic function, we can represent tan 28° as, tan 28 degrees = tan(28° + n × 180°), n ∈ Z.
⇒ tan 28° = tan 208° = tan 388°, and so on.
Note: Since, tangent is an odd function, the value of tan(-28°) = -tan(28°).

Methods to Find Value of Tan 28 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 28° is given as 0.53170. . .. We can find the value of tan 28 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 28° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 28 degrees as:

• sin(28°)/cos(28°)
• ± sin 28°/√(1 - sin²(28°))
• ± √(1 - cos²(28°))/cos 28°
• ± 1/√(cosec²(28°) - 1)
• ± √(sec²(28°) - 1)
• 1/cot 28°

Note: Since 28° lies in the 1st Quadrant, the final value of tan 28° will be positive.

We can use trigonometric identities to represent tan 28° as,

• cot(90° - 28°) = cot 62°
• -cot(90° + 28°) = -cot 118°
• -tan (180° - 28°) = -tan 152°

Tan 28 Degrees Using Unit Circle

To find the value of tan 28 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 28° angle with the positive x-axis.
• The tan of 28 degrees equals the y-coordinate(0.4695) divided by x-coordinate(0.8829) of the point of intersection (0.8829, 0.4695) of unit circle and r.

Hence the value of tan 28° = y/x = 0.5317 (approx).

☛ Also Check:

• tan 105 degrees
• tan 2 degrees
• tan 12 degrees
• tan 100 degrees
• tan 54 degrees
• tan 62 degrees

FAQs on Tan 28 Degrees

What is Tan 28 Degrees?

Tan 28 degrees is the value of tangent trigonometric function for an angle equal to 28 degrees. The value of tan 28° is 0.5317 (approx).

How to Find Tan 28° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 28° can be given in terms of other trigonometric functions as:

• sin(28°)/cos(28°)
• ± sin 28°/√(1 - sin²(28°))
• ± √(1 - cos²(28°))/cos 28°
• ± 1/√(cosec²(28°) - 1)
• ± √(sec²(28°) - 1)
• 1/cot 28°

☛ Also check: trigonometric table

What is the Value of Tan 28 Degrees in Terms of Cos 28°?

We know, using trig identities, we can write tan 28° as √(1 - cos²(28°))/cos 28°. Here, the value of cos 28° is equal to 0.882947.

How to Find the Value of Tan 28 Degrees?

The value of tan 28 degrees can be calculated by constructing an angle of 28° with the x-axis, and then finding the coordinates of the corresponding point (0.8829, 0.4695) on the unit circle. The value of tan 28° is equal to the y-coordinate(0.4695) divided by the x-coordinate (0.8829). ∴ tan 28° = 0.5317

What is the Value of Tan 28° in Terms of Sec 28°?

We can represent the tangent function in terms of the secant function using trig identities, tan 28° can be written as √(sec²(28°) - 1). Here, the value of sec 28° is equal to 1.1325.