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Tan 56 Degrees

The value of tan 56 degrees is 1.4825609. . .. Tan 56 degrees in radians is written as tan (56° × π/180°), i.e., tan (14π/45) or tan (0.977384. . .). In this article, we will discuss the methods to find the value of tan 56 degrees with examples.

Tan 56° in decimal: 1.4825609. . .
Tan (-56 degrees): -1.4825609. . .
Tan 56° in radians: tan (14π/45) or tan (0.9773843 . . .)

What is the Value of Tan 56 Degrees?

The value of tan 56 degrees in decimal is 1.482560968. . .. Tan 56 degrees can also be expressed using the equivalent of the given angle (56 degrees) in radians (0.97738 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 56 degrees = 56° × (π/180°) rad = 14π/45 or 0.9773 . . .
∴ tan 56° = tan(0.9773) = 1.4825609. . .

Explanation:

For tan 56 degrees, the angle 56° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 56° value = 1.4825609. . .
Since the tangent function is a periodic function, we can represent tan 56° as, tan 56 degrees = tan(56° + n × 180°), n ∈ Z.
⇒ tan 56° = tan 236° = tan 416°, and so on.
Note: Since, tangent is an odd function, the value of tan(-56°) = -tan(56°).

Methods to Find Value of Tan 56 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 56° is given as 1.48256. . .. We can find the value of tan 56 degrees by:

Using Unit Circle
Using Trigonometric Functions

Tan 56 Degrees Using Unit Circle

To find the value of tan 56 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 56° angle with the positive x-axis.
The tan of 56 degrees equals the y-coordinate(0.829) divided by x-coordinate(0.5592) of the point of intersection (0.5592, 0.829) of unit circle and r.

Hence the value of tan 56° = y/x = 1.4826 (approx).

Tan 56° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 56 degrees as:

sin(56°)/cos(56°)
± sin 56°/√(1 - sin²(56°))
± √(1 - cos²(56°))/cos 56°
± 1/√(cosec²(56°) - 1)
± √(sec²(56°) - 1)
1/cot 56°

Note: Since 56° lies in the 1st Quadrant, the final value of tan 56° will be positive.

We can use trigonometric identities to represent tan 56° as,

cot(90° - 56°) = cot 34°
-cot(90° + 56°) = -cot 146°
-tan (180° - 56°) = -tan 124°

☛ Also Check:

Examples Using Tan 56 Degrees

Example 1: Using the value of tan 56°, solve: (sec²(56°) - 1).

Solution:
We know, (sec²(56°) - 1) = (tan²(56°)) = 2.198
⇒ (sec²(56°) - 1) = 2.198
Example 2: Find the value of 5 tan(56°)/9 tan(124°).

Solution:

Using trigonometric identities, we know, tan(56°) = -tan(180° - 56°) = -tan 124°.
⇒ tan(56°) = -tan(124°)
⇒ Value of 5 tan(56°)/9 tan(124°) = -5/9
Example 3: Simplify: 3 (tan 56°/cot 34°)

Solution:

We know tan 56° = cot 34°
⇒ 3 tan 56°/cot 34° = 3 (tan 56°/tan 56°)
= 3(1) = 3

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FAQs on Tan 56 Degrees

What is Tan 56 Degrees?

Tan 56 degrees is the value of tangent trigonometric function for an angle equal to 56 degrees. The value of tan 56° is 1.4826 (approx).

What is the Value of Tan 56° in Terms of Cosec 56°?

Since the tangent function can be represented using the cosecant function, we can write tan 56° as 1/√(cosec²(56°) - 1). The value of cosec 56° is equal to 1.20621.

How to Find the Value of Tan 56 Degrees?

The value of tan 56 degrees can be calculated by constructing an angle of 56° with the x-axis, and then finding the coordinates of the corresponding point (0.5592, 0.829) on the unit circle. The value of tan 56° is equal to the y-coordinate(0.829) divided by the x-coordinate (0.5592). ∴ tan 56° = 1.4826

How to Find Tan 56° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 56° can be given in terms of other trigonometric functions as:

sin(56°)/cos(56°)
± sin 56°/√(1 - sin²(56°))
± √(1 - cos²(56°))/cos 56°
± 1/√(cosec²(56°) - 1)
± √(sec²(56°) - 1)
1/cot 56°

☛ Also check: trigonometry table

What is the Value of Tan 56 Degrees in Terms of Cot 56°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 56° as 1/cot(56°). The value of cot 56° is equal to 0.67450.

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