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Tan 58 Degrees

The value of tan 58 degrees is 1.6003345. . .. Tan 58 degrees in radians is written as tan (58° × π/180°), i.e., tan (29π/90) or tan (1.012290. . .). In this article, we will discuss the methods to find the value of tan 58 degrees with examples.

Tan 58° in decimal: 1.6003345. . .
Tan (-58 degrees): -1.6003345. . .
Tan 58° in radians: tan (29π/90) or tan (1.0122909 . . .)

What is the Value of Tan 58 Degrees?

The value of tan 58 degrees in decimal is 1.600334529. . .. Tan 58 degrees can also be expressed using the equivalent of the given angle (58 degrees) in radians (1.01229 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 58 degrees = 58° × (π/180°) rad = 29π/90 or 1.0122 . . .
∴ tan 58° = tan(1.0122) = 1.6003345. . .

Explanation:

For tan 58 degrees, the angle 58° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 58° value = 1.6003345. . .
Since the tangent function is a periodic function, we can represent tan 58° as, tan 58 degrees = tan(58° + n × 180°), n ∈ Z.
⇒ tan 58° = tan 238° = tan 418°, and so on.
Note: Since, tangent is an odd function, the value of tan(-58°) = -tan(58°).

Methods to Find Value of Tan 58 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 58° is given as 1.60033. . .. We can find the value of tan 58 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 58° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 58 degrees as:

sin(58°)/cos(58°)
± sin 58°/√(1 - sin²(58°))
± √(1 - cos²(58°))/cos 58°
± 1/√(cosec²(58°) - 1)
± √(sec²(58°) - 1)
1/cot 58°

Note: Since 58° lies in the 1st Quadrant, the final value of tan 58° will be positive.

We can use trigonometric identities to represent tan 58° as,

cot(90° - 58°) = cot 32°
-cot(90° + 58°) = -cot 148°
-tan (180° - 58°) = -tan 122°

Tan 58 Degrees Using Unit Circle

To find the value of tan 58 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 58° angle with the positive x-axis.
The tan of 58 degrees equals the y-coordinate(0.848) divided by x-coordinate(0.5299) of the point of intersection (0.5299, 0.848) of unit circle and r.

Hence the value of tan 58° = y/x = 1.6003 (approx).

☛ Also Check:

Examples Using Tan 58 Degrees

Example 1: Simplify: 9 (tan 58°/cot 32°)

Solution:

We know tan 58° = cot 32°
⇒ 9 tan 58°/cot 32° = 9 (tan 58°/tan 58°)
= 9(1) = 9
Example 2: Find the value of (2 sin (29°) cos (29°) sec (58°)). [Hint: Use tan 58° = 1.6003]

Solution:

Using sin 2a formula,
2 sin (29°) cos (29°) = sin (2 × 29°) = sin 58°
⇒ 2 sin (29°) cos (29°) sec(58°) = sin 58° sec 58°
= sin 58°/cos 58° = tan 58°
⇒ (2 sin (29°) cos (29°) sec(58°)) = 1.6003
Example 3: Using the value of tan 58°, solve: (sec²(58°) - 1).

Solution:
We know, (sec²(58°) - 1) = (tan²(58°)) = 2.5611
⇒ (sec²(58°) - 1) = 2.5611

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FAQs on Tan 58 Degrees

What is Tan 58 Degrees?

Tan 58 degrees is the value of tangent trigonometric function for an angle equal to 58 degrees. The value of tan 58° is 1.6003 (approx).

What is the Value of Tan 58 Degrees in Terms of Cos 58°?

We know, using trig identities, we can write tan 58° as √(1 - cos²(58°))/cos 58°. Here, the value of cos 58° is equal to 0.529919.

What is the Value of Tan 58° in Terms of Sec 58°?

We can represent the tangent function in terms of the secant function using trig identities, tan 58° can be written as √(sec²(58°) - 1). Here, the value of sec 58° is equal to 1.8870.

How to Find the Value of Tan 58 Degrees?

The value of tan 58 degrees can be calculated by constructing an angle of 58° with the x-axis, and then finding the coordinates of the corresponding point (0.5299, 0.848) on the unit circle. The value of tan 58° is equal to the y-coordinate(0.848) divided by the x-coordinate (0.5299). ∴ tan 58° = 1.6003

How to Find Tan 58° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 58° can be given in terms of other trigonometric functions as:

sin(58°)/cos(58°)
± sin 58°/√(1 - sin²(58°))
± √(1 - cos²(58°))/cos 58°
± 1/√(cosec²(58°) - 1)
± √(sec²(58°) - 1)
1/cot 58°

☛ Also check: trigonometry table

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