Tan 69 Degrees

The value of tan 69 degrees is 2.6050890. . .. Tan 69 degrees in radians is written as tan (69° × π/180°), i.e., tan (23π/60) or tan (1.204277. . .). In this article, we will discuss the methods to find the value of tan 69 degrees with examples.

• Tan 69° in decimal: 2.6050890. . .
• Tan (-69 degrees): -2.6050890. . .
• Tan 69° in radians: tan (23π/60) or tan (1.2042771 . . .)

What is the Value of Tan 69 Degrees?

The value of tan 69 degrees in decimal is 2.605089064. . .. Tan 69 degrees can also be expressed using the equivalent of the given angle (69 degrees) in radians (1.20427 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 69 degrees = 69° × (π/180°) rad = 23π/60 or 1.2042 . . .
∴ tan 69° = tan(1.2042) = 2.6050890. . .

Explanation:

For tan 69 degrees, the angle 69° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 69° value = 2.6050890. . .
Since the tangent function is a periodic function, we can represent tan 69° as, tan 69 degrees = tan(69° + n × 180°), n ∈ Z.
⇒ tan 69° = tan 249° = tan 429°, and so on.
Note: Since, tangent is an odd function, the value of tan(-69°) = -tan(69°).

Methods to Find Value of Tan 69 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 69° is given as 2.60508. . .. We can find the value of tan 69 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 69 Degrees Using Unit Circle

To find the value of tan 69 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 69° angle with the positive x-axis.
• The tan of 69 degrees equals the y-coordinate(0.9336) divided by x-coordinate(0.3584) of the point of intersection (0.3584, 0.9336) of unit circle and r.

Hence the value of tan 69° = y/x = 2.6051 (approx).

Tan 69° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 69 degrees as:

• sin(69°)/cos(69°)
• ± sin 69°/√(1 - sin²(69°))
• ± √(1 - cos²(69°))/cos 69°
• ± 1/√(cosec²(69°) - 1)
• ± √(sec²(69°) - 1)
• 1/cot 69°

Note: Since 69° lies in the 1st Quadrant, the final value of tan 69° will be positive.

We can use trigonometric identities to represent tan 69° as,

• cot(90° - 69°) = cot 21°
• -cot(90° + 69°) = -cot 159°
• -tan (180° - 69°) = -tan 111°

☛ Also Check:

• tan 37 degrees
• tan 40 degrees
• tan 53 degrees
• tan 285 degrees
• tan 13 degrees
• tan 390 degrees

FAQs on Tan 69 Degrees

What is Tan 69 Degrees?

Tan 69 degrees is the value of tangent trigonometric function for an angle equal to 69 degrees. The value of tan 69° is 2.6051 (approx).

What is the Value of Tan 69 Degrees in Terms of Sin 69°?

Using trigonometric identities, we can write tan 69° in terms of sin 69° as, tan(69°) = sin 69°/√(1 - sin²(69°)) . Here, the value of sin 69° is equal to 0.9336.

What is the Value of Tan 69° in Terms of Cosec 69°?

Since the tangent function can be represented using the cosecant function, we can write tan 69° as 1/√(cosec²(69°) - 1). The value of cosec 69° is equal to 1.07114.

How to Find Tan 69° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 69° can be given in terms of other trigonometric functions as:

• sin(69°)/cos(69°)
• ± sin 69°/√(1 - sin²(69°))
• ± √(1 - cos²(69°))/cos 69°
• ± 1/√(cosec²(69°) - 1)
• ± √(sec²(69°) - 1)
• 1/cot 69°

☛ Also check: trigonometry table

How to Find the Value of Tan 69 Degrees?

The value of tan 69 degrees can be calculated by constructing an angle of 69° with the x-axis, and then finding the coordinates of the corresponding point (0.3584, 0.9336) on the unit circle. The value of tan 69° is equal to the y-coordinate(0.9336) divided by the x-coordinate (0.3584). ∴ tan 69° = 2.6051