Tan 59 Degrees

The value of tan 59 degrees is 1.6642794. . .. Tan 59 degrees in radians is written as tan (59° × π/180°), i.e., tan (1.029744. . .). In this article, we will discuss the methods to find the value of tan 59 degrees with examples.

• Tan 59° in decimal: 1.6642794. . .
• Tan (-59 degrees): -1.6642794. . .
• Tan 59° in radians: tan (1.0297442 . . .)

What is the Value of Tan 59 Degrees?

The value of tan 59 degrees in decimal is 1.664279482. . .. Tan 59 degrees can also be expressed using the equivalent of the given angle (59 degrees) in radians (1.02974 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 59 degrees = 59° × (π/180°) rad = 1.0297 . . .
∴ tan 59° = tan(1.0297) = 1.6642794. . .

Explanation:

For tan 59 degrees, the angle 59° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 59° value = 1.6642794. . .
Since the tangent function is a periodic function, we can represent tan 59° as, tan 59 degrees = tan(59° + n × 180°), n ∈ Z.
⇒ tan 59° = tan 239° = tan 419°, and so on.
Note: Since, tangent is an odd function, the value of tan(-59°) = -tan(59°).

Methods to Find Value of Tan 59 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 59° is given as 1.66427. . .. We can find the value of tan 59 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 59° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 59 degrees as:

• sin(59°)/cos(59°)
• ± sin 59°/√(1 - sin²(59°))
• ± √(1 - cos²(59°))/cos 59°
• ± 1/√(cosec²(59°) - 1)
• ± √(sec²(59°) - 1)
• 1/cot 59°

Note: Since 59° lies in the 1st Quadrant, the final value of tan 59° will be positive.

We can use trigonometric identities to represent tan 59° as,

• cot(90° - 59°) = cot 31°
• -cot(90° + 59°) = -cot 149°
• -tan (180° - 59°) = -tan 121°

Tan 59 Degrees Using Unit Circle

To find the value of tan 59 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 59° angle with the positive x-axis.
• The tan of 59 degrees equals the y-coordinate(0.8572) divided by x-coordinate(0.515) of the point of intersection (0.515, 0.8572) of unit circle and r.

Hence the value of tan 59° = y/x = 1.6643 (approx).

☛ Also Check:

• tan 53 degrees
• tan 1 degrees
• tan 270 degrees
• tan 70 degrees
• tan 300 degrees
• tan 405 degrees

FAQs on Tan 59 Degrees

What is Tan 59 Degrees?

Tan 59 degrees is the value of tangent trigonometric function for an angle equal to 59 degrees. The value of tan 59° is 1.6643 (approx).

What is the Value of Tan 59 Degrees in Terms of Sin 59°?

Using trigonometric identities, we can write tan 59° in terms of sin 59° as, tan(59°) = sin 59°/√(1 - sin²(59°)) . Here, the value of sin 59° is equal to 0.8572.

How to Find the Value of Tan 59 Degrees?

The value of tan 59 degrees can be calculated by constructing an angle of 59° with the x-axis, and then finding the coordinates of the corresponding point (0.515, 0.8572) on the unit circle. The value of tan 59° is equal to the y-coordinate(0.8572) divided by the x-coordinate (0.515). ∴ tan 59° = 1.6643

How to Find Tan 59° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 59° can be given in terms of other trigonometric functions as:

• sin(59°)/cos(59°)
• ± sin 59°/√(1 - sin²(59°))
• ± √(1 - cos²(59°))/cos 59°
• ± 1/√(cosec²(59°) - 1)
• ± √(sec²(59°) - 1)
• 1/cot 59°

☛ Also check: trigonometric table

What is the Value of Tan 59° in Terms of Cosec 59°?

Since the tangent function can be represented using the cosecant function, we can write tan 59° as 1/√(cosec²(59°) - 1). The value of cosec 59° is equal to 1.16663.