Tan 76 Degrees

The value of tan 76 degrees is 4.0107809. . .. Tan 76 degrees in radians is written as tan (76° × π/180°), i.e., tan (19π/45) or tan (1.326450. . .). In this article, we will discuss the methods to find the value of tan 76 degrees with examples.

• Tan 76° in decimal: 4.0107809. . .
• Tan (-76 degrees): -4.0107809. . .
• Tan 76° in radians: tan (19π/45) or tan (1.3264502 . . .)

What is the Value of Tan 76 Degrees?

The value of tan 76 degrees in decimal is 4.010780933. . .. Tan 76 degrees can also be expressed using the equivalent of the given angle (76 degrees) in radians (1.32645 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 76 degrees = 76° × (π/180°) rad = 19π/45 or 1.3264 . . .
∴ tan 76° = tan(1.3264) = 4.0107809. . .

Explanation:

For tan 76 degrees, the angle 76° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 76° value = 4.0107809. . .
Since the tangent function is a periodic function, we can represent tan 76° as, tan 76 degrees = tan(76° + n × 180°), n ∈ Z.
⇒ tan 76° = tan 256° = tan 436°, and so on.
Note: Since, tangent is an odd function, the value of tan(-76°) = -tan(76°).

Methods to Find Value of Tan 76 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 76° is given as 4.01078. . .. We can find the value of tan 76 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 76 Degrees Using Unit Circle

To find the value of tan 76 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 76° angle with the positive x-axis.
• The tan of 76 degrees equals the y-coordinate(0.9703) divided by x-coordinate(0.2419) of the point of intersection (0.2419, 0.9703) of unit circle and r.

Hence the value of tan 76° = y/x = 4.0108 (approx).

Tan 76° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 76 degrees as:

• sin(76°)/cos(76°)
• ± sin 76°/√(1 - sin²(76°))
• ± √(1 - cos²(76°))/cos 76°
• ± 1/√(cosec²(76°) - 1)
• ± √(sec²(76°) - 1)
• 1/cot 76°

Note: Since 76° lies in the 1st Quadrant, the final value of tan 76° will be positive.

We can use trigonometric identities to represent tan 76° as,

• cot(90° - 76°) = cot 14°
• -cot(90° + 76°) = -cot 166°
• -tan (180° - 76°) = -tan 104°

☛ Also Check:

• tan 40 degrees
• tan 60 degrees
• tan 105 degrees
• tan 82 degrees
• tan 285 degrees
• tan 86 degrees

FAQs on Tan 76 Degrees

What is Tan 76 Degrees?

Tan 76 degrees is the value of tangent trigonometric function for an angle equal to 76 degrees. The value of tan 76° is 4.0108 (approx).

What is the Value of Tan 76 Degrees in Terms of Sin 76°?

Using trigonometric identities, we can write tan 76° in terms of sin 76° as, tan(76°) = sin 76°/√(1 - sin²(76°)) . Here, the value of sin 76° is equal to 0.9703.

How to Find Tan 76° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 76° can be given in terms of other trigonometric functions as:

• sin(76°)/cos(76°)
• ± sin 76°/√(1 - sin²(76°))
• ± √(1 - cos²(76°))/cos 76°
• ± 1/√(cosec²(76°) - 1)
• ± √(sec²(76°) - 1)
• 1/cot 76°

☛ Also check: trigonometric table

How to Find the Value of Tan 76 Degrees?

The value of tan 76 degrees can be calculated by constructing an angle of 76° with the x-axis, and then finding the coordinates of the corresponding point (0.2419, 0.9703) on the unit circle. The value of tan 76° is equal to the y-coordinate(0.9703) divided by the x-coordinate (0.2419). ∴ tan 76° = 4.0108

What is the Exact Value of tan 76 Degrees?

The exact value of tan 76 degrees can be given accurately up to 8 decimal places as 4.01078093.