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Tan 57 Degrees

The value of tan 57 degrees is 1.5398649. . .. Tan 57 degrees in radians is written as tan (57° × π/180°), i.e., tan (19π/60) or tan (0.994837. . .). In this article, we will discuss the methods to find the value of tan 57 degrees with examples.

Tan 57° in decimal: 1.5398649. . .
Tan (-57 degrees): -1.5398649. . .
Tan 57° in radians: tan (19π/60) or tan (0.9948376 . . .)

What is the Value of Tan 57 Degrees?

The value of tan 57 degrees in decimal is 1.539864963. . .. Tan 57 degrees can also be expressed using the equivalent of the given angle (57 degrees) in radians (0.99483 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 57 degrees = 57° × (π/180°) rad = 19π/60 or 0.9948 . . .
∴ tan 57° = tan(0.9948) = 1.5398649. . .

Explanation:

For tan 57 degrees, the angle 57° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 57° value = 1.5398649. . .
Since the tangent function is a periodic function, we can represent tan 57° as, tan 57 degrees = tan(57° + n × 180°), n ∈ Z.
⇒ tan 57° = tan 237° = tan 417°, and so on.
Note: Since, tangent is an odd function, the value of tan(-57°) = -tan(57°).

Methods to Find Value of Tan 57 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 57° is given as 1.53986. . .. We can find the value of tan 57 degrees by:

Using Unit Circle
Using Trigonometric Functions

Tan 57 Degrees Using Unit Circle

To find the value of tan 57 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 57° angle with the positive x-axis.
The tan of 57 degrees equals the y-coordinate(0.8387) divided by x-coordinate(0.5446) of the point of intersection (0.5446, 0.8387) of unit circle and r.

Hence the value of tan 57° = y/x = 1.5399 (approx).

Tan 57° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 57 degrees as:

sin(57°)/cos(57°)
± sin 57°/√(1 - sin²(57°))
± √(1 - cos²(57°))/cos 57°
± 1/√(cosec²(57°) - 1)
± √(sec²(57°) - 1)
1/cot 57°

Note: Since 57° lies in the 1st Quadrant, the final value of tan 57° will be positive.

We can use trigonometric identities to represent tan 57° as,

cot(90° - 57°) = cot 33°
-cot(90° + 57°) = -cot 147°
-tan (180° - 57°) = -tan 123°

☛ Also Check:

Examples Using Tan 57 Degrees

Example 1: Find the value of 5 tan(57°)/6 tan(123°).

Solution:

Using trigonometric identities, we know, tan(57°) = -tan(180° - 57°) = -tan 123°.
⇒ tan(57°) = -tan(123°)
⇒ Value of 5 tan(57°)/6 tan(123°) = -5/6
Example 2: Simplify: 4 (tan 57°/cot 33°)

Solution:

We know tan 57° = cot 33°
⇒ 4 tan 57°/cot 33° = 4 (tan 57°/tan 57°)
= 4(1) = 4
Example 3: Find the value of (2 sin (28.5°) cos (28.5°) sec (57°)). [Hint: Use tan 57° = 1.5399]

Solution:

Using sin 2a formula,
2 sin (28.5°) cos (28.5°) = sin (2 × 28.5°) = sin 57°
⇒ 2 sin (28.5°) cos (28.5°) sec(57°) = sin 57° sec 57°
= sin 57°/cos 57° = tan 57°
⇒ (2 sin (28.5°) cos (28.5°) sec(57°)) = 1.5399

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FAQs on Tan 57 Degrees

What is Tan 57 Degrees?

Tan 57 degrees is the value of tangent trigonometric function for an angle equal to 57 degrees. The value of tan 57° is 1.5399 (approx).

How to Find the Value of Tan 57 Degrees?

The value of tan 57 degrees can be calculated by constructing an angle of 57° with the x-axis, and then finding the coordinates of the corresponding point (0.5446, 0.8387) on the unit circle. The value of tan 57° is equal to the y-coordinate(0.8387) divided by the x-coordinate (0.5446). ∴ tan 57° = 1.5399

What is the Value of Tan 57° in Terms of Cosec 57°?

Since the tangent function can be represented using the cosecant function, we can write tan 57° as 1/√(cosec²(57°) - 1). The value of cosec 57° is equal to 1.19236.

What is the Value of Tan 57 Degrees in Terms of Cot 57°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 57° as 1/cot(57°). The value of cot 57° is equal to 0.64940.

How to Find Tan 57° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 57° can be given in terms of other trigonometric functions as:

sin(57°)/cos(57°)
± sin 57°/√(1 - sin²(57°))
± √(1 - cos²(57°))/cos 57°
± 1/√(cosec²(57°) - 1)
± √(sec²(57°) - 1)
1/cot 57°

☛ Also check: trigonometric table

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