Tan 51 Degrees

The value of tan 51 degrees is 1.2348971. . .. Tan 51 degrees in radians is written as tan (51° × π/180°), i.e., tan (17π/60) or tan (0.890117. . .). In this article, we will discuss the methods to find the value of tan 51 degrees with examples.

• Tan 51° in decimal: 1.2348971. . .
• Tan (-51 degrees): -1.2348971. . .
• Tan 51° in radians: tan (17π/60) or tan (0.8901179 . . .)

What is the Value of Tan 51 Degrees?

The value of tan 51 degrees in decimal is 1.234897156. . .. Tan 51 degrees can also be expressed using the equivalent of the given angle (51 degrees) in radians (0.89011 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 51 degrees = 51° × (π/180°) rad = 17π/60 or 0.8901 . . .
∴ tan 51° = tan(0.8901) = 1.2348971. . .

Explanation:

For tan 51 degrees, the angle 51° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 51° value = 1.2348971. . .
Since the tangent function is a periodic function, we can represent tan 51° as, tan 51 degrees = tan(51° + n × 180°), n ∈ Z.
⇒ tan 51° = tan 231° = tan 411°, and so on.
Note: Since, tangent is an odd function, the value of tan(-51°) = -tan(51°).

Methods to Find Value of Tan 51 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 51° is given as 1.23489. . .. We can find the value of tan 51 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 51 Degrees Using Unit Circle

To find the value of tan 51 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 51° angle with the positive x-axis.
• The tan of 51 degrees equals the y-coordinate(0.7771) divided by x-coordinate(0.6293) of the point of intersection (0.6293, 0.7771) of unit circle and r.

Hence the value of tan 51° = y/x = 1.2349 (approx).

Tan 51° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 51 degrees as:

• sin(51°)/cos(51°)
• ± sin 51°/√(1 - sin²(51°))
• ± √(1 - cos²(51°))/cos 51°
• ± 1/√(cosec²(51°) - 1)
• ± √(sec²(51°) - 1)
• 1/cot 51°

Note: Since 51° lies in the 1st Quadrant, the final value of tan 51° will be positive.

We can use trigonometric identities to represent tan 51° as,

• cot(90° - 51°) = cot 39°
• -cot(90° + 51°) = -cot 141°
• -tan (180° - 51°) = -tan 129°

☛ Also Check:

• tan 90 degrees
• tan 1 degrees
• tan 10 degrees
• tan 300 degrees
• tan 59 degrees
• tan 11 degrees

FAQs on Tan 51 Degrees

What is Tan 51 Degrees?

Tan 51 degrees is the value of tangent trigonometric function for an angle equal to 51 degrees. The value of tan 51° is 1.2349 (approx).

How to Find the Value of Tan 51 Degrees?

The value of tan 51 degrees can be calculated by constructing an angle of 51° with the x-axis, and then finding the coordinates of the corresponding point (0.6293, 0.7771) on the unit circle. The value of tan 51° is equal to the y-coordinate(0.7771) divided by the x-coordinate (0.6293). ∴ tan 51° = 1.2349

What is the Value of Tan 51° in Terms of Sec 51°?

We can represent the tangent function in terms of the secant function using trig identities, tan 51° can be written as √(sec²(51°) - 1). Here, the value of sec 51° is equal to 1.5890.

How to Find Tan 51° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 51° can be given in terms of other trigonometric functions as:

• sin(51°)/cos(51°)
• ± sin 51°/√(1 - sin²(51°))
• ± √(1 - cos²(51°))/cos 51°
• ± 1/√(cosec²(51°) - 1)
• ± √(sec²(51°) - 1)
• 1/cot 51°

☛ Also check: trigonometric table

What is the Value of Tan 51 Degrees in Terms of Cos 51°?

We know, using trig identities, we can write tan 51° as √(1 - cos²(51°))/cos 51°. Here, the value of cos 51° is equal to 0.629320.