Tan 53 Degrees

The value of tan 53 degrees is 1.3270448. . .. Tan 53 degrees in radians is written as tan (53° × π/180°), i.e., tan (0.925024. . .). In this article, we will discuss the methods to find the value of tan 53 degrees with examples.

• Tan 53° in decimal: 1.3270448. . .
• Tan (-53 degrees): -1.3270448. . .
• Tan 53° in radians: tan (0.9250245 . . .)

What is the Value of Tan 53 Degrees?

The value of tan 53 degrees in decimal is 1.327044821. . .. Tan 53 degrees can also be expressed using the equivalent of the given angle (53 degrees) in radians (0.92502 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 53 degrees = 53° × (π/180°) rad = 0.9250 . . .
∴ tan 53° = tan(0.9250) = 1.3270448. . .

Explanation:

For tan 53 degrees, the angle 53° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 53° value = 1.3270448. . .
Since the tangent function is a periodic function, we can represent tan 53° as, tan 53 degrees = tan(53° + n × 180°), n ∈ Z.
⇒ tan 53° = tan 233° = tan 413°, and so on.
Note: Since, tangent is an odd function, the value of tan(-53°) = -tan(53°).

Methods to Find Value of Tan 53 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 53° is given as 1.32704. . .. We can find the value of tan 53 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 53° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 53 degrees as:

• sin(53°)/cos(53°)
• ± sin 53°/√(1 - sin²(53°))
• ± √(1 - cos²(53°))/cos 53°
• ± 1/√(cosec²(53°) - 1)
• ± √(sec²(53°) - 1)
• 1/cot 53°

Note: Since 53° lies in the 1st Quadrant, the final value of tan 53° will be positive.

We can use trigonometric identities to represent tan 53° as,

• cot(90° - 53°) = cot 37°
• -cot(90° + 53°) = -cot 143°
• -tan (180° - 53°) = -tan 127°

Tan 53 Degrees Using Unit Circle

To find the value of tan 53 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 53° angle with the positive x-axis.
• The tan of 53 degrees equals the y-coordinate(0.7986) divided by x-coordinate(0.6018) of the point of intersection (0.6018, 0.7986) of unit circle and r.

Hence the value of tan 53° = y/x = 1.327 (approx).

☛ Also Check:

• tan 225 degrees
• tan 270 degrees
• tan 135 degrees
• tan 36 degrees
• tan 540 degrees
• tan 31 degrees

FAQs on Tan 53 Degrees

What is Tan 53 Degrees?

Tan 53 degrees is the value of tangent trigonometric function for an angle equal to 53 degrees. The value of tan 53° is 1.327 (approx).

What is the Value of Tan 53 Degrees in Terms of Cot 53°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 53° as 1/cot(53°). The value of cot 53° is equal to 0.75355.

How to Find Tan 53° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 53° can be given in terms of other trigonometric functions as:

• sin(53°)/cos(53°)
• ± sin 53°/√(1 - sin²(53°))
• ± √(1 - cos²(53°))/cos 53°
• ± 1/√(cosec²(53°) - 1)
• ± √(sec²(53°) - 1)
• 1/cot 53°

☛ Also check: trigonometry table

What is the Exact Value of tan 53 Degrees?

The exact value of tan 53 degrees can be given accurately up to 8 decimal places as 1.32704482.

How to Find the Value of Tan 53 Degrees?

The value of tan 53 degrees can be calculated by constructing an angle of 53° with the x-axis, and then finding the coordinates of the corresponding point (0.6018, 0.7986) on the unit circle. The value of tan 53° is equal to the y-coordinate(0.7986) divided by the x-coordinate (0.6018). ∴ tan 53° = 1.327