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Tan 1290 Degrees

The value of tan 1290 degrees is 0.5773502. . .. Tan 1290 degrees in radians is written as tan (1290° × π/180°), i.e., tan (43π/6) or tan (22.514747. . .). In this article, we will discuss the methods to find the value of tan 1290 degrees with examples.

Tan 1290°: 1/√3
Tan 1290° in decimal: 0.5773502. . .
Tan (-1290 degrees): -0.5773502. . . or -1/√3
Tan 1290° in radians: tan (43π/6) or tan (22.5147473 . . .)

What is the Value of Tan 1290 Degrees?

The value of tan 1290 degrees in decimal is 0.577350269. . .. Tan 1290 degrees can also be expressed using the equivalent of the given angle (1290 degrees) in radians (22.51474 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1290 degrees = 1290° × (π/180°) rad = 43π/6 or 22.5147 . . .
∴ tan 1290° = tan(22.5147) = 1/√3 or 0.5773502. . .

Explanation:

For tan 1290°, the angle 1290° > 360°. We can represent tan 1290° as, tan(1290° mod 360°) = tan(210°). The angle 1290°, coterminal to angle 210°, is located in the Third Quadrant(Quadrant III).
Since tangent function is positive in the 3rd quadrant, thus tan 1290 degrees value = 1/√3 or 0.5773502. . .
Similarly, given the periodic property of tan 1290°, it can also be written as, tan 1290 degrees = (1290° + n × 180°), n ∈ Z.
⇒ tan 1290° = tan 1470° = tan 1650°, and so on.
Note: Since, tangent is an odd function, the value of tan(-1290°) = -tan(1290°).

Methods to Find Value of Tan 1290 Degrees

The tangent function is positive in the 3rd quadrant. The value of tan 1290° is given as 0.57735. . .. We can find the value of tan 1290 degrees by:

Using Unit Circle
Using Trigonometric Functions

Tan 1290 Degrees Using Unit Circle

To find the value of tan 1290 degrees using the unit circle, represent 1290° in the form (3 × 360°) + 210° [∵ 1290°>360°] ∵ The angle 1290° is coterminal to 210° angle and also tangent is a periodic function, tan 1290° = tan 210°.

Rotate ‘r’ anticlockwise to form 210° or 1290° angle with the positive x-axis.
The tan of 1290 degrees equals the y-coordinate(-0.5) divided by x-coordinate(-0.866) of the point of intersection (-0.866, -0.5) of unit circle and r.

Hence the value of tan 1290° = y/x = 0.5774 (approx).

Tan 1290° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 1290 degrees as:

sin(1290°)/cos(1290°)
± sin 1290°/√(1 - sin²(1290°))
± √(1 - cos²(1290°))/cos 1290°
± 1/√(cosec²(1290°) - 1)
± √(sec²(1290°) - 1)
1/cot 1290°

Note: Since 1290° lies in the 3rd Quadrant, the final value of tan 1290° will be positive.

We can use trigonometric identities to represent tan 1290° as,

cot(90° - 1290°) = cot(-1200°)
-cot(90° + 1290°) = -cot 1380°
-tan (180° - 1290°) = -tan(-1110°)

☛ Also Check:

Examples Using Tan 1290 Degrees

Example 1: Find the value of tan 1290° if cot 1290° is 1.7320.

Solution:
Since, tan 1290° = 1/cot 1290°
⇒ tan 1290° = 1/1.7320 = 0.5774
Example 2: Simplify: 4 (tan 1290°/cot(-1200°))

Solution:

We know tan 1290° = cot(-1200°)
⇒ 4 tan 1290°/cot(-1200°) = 4 (tan 1290°/tan 1290°)
= 4(1) = 4
Example 3: Find the value of 2 tan 645°/(1 - tan²(645°)). [Hint: Use tan 1290° = 0.5774]

Solution:

Using the tan 2a formula,
2 tan 645°/(1 - tan²(645°)) = tan(2 × 645°) = tan 1290°
∵ tan 1290° = 0.5774
⇒ 2 tan 645°/(1 - tan²(645°)) = 0.5774

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FAQs on Tan 1290 Degrees

What is Tan 1290 Degrees?

Tan 1290 degrees is the value of tangent trigonometric function for an angle equal to 1290 degrees. The value of tan 1290° is 1/√3 or 0.5774 (approx).

How to Find the Value of Tan 1290 Degrees?

The value of tan 1290 degrees can be calculated by constructing an angle of 1290° with the x-axis, and then finding the coordinates of the corresponding point (-0.866, -0.5) on the unit circle. The value of tan 1290° is equal to the y-coordinate(-0.5) divided by the x-coordinate (-0.866). ∴ tan 1290° = 1/√3 or 0.5774

What is the Value of Tan 1290 Degrees in Terms of Cos 1290°?

We know, using trig identities, we can write tan 1290° as -√(1 - cos²(1290°))/cos 1290°. Here, the value of cos 1290° is equal to -0.866025.

What is the Value of Tan 1290° in Terms of Cosec 1290°?

Since the tangent function can be represented using the cosecant function, we can write tan 1290° as 1/√(cosec²(1290°) - 1). The value of cosec 1290° is equal to -2.

How to Find Tan 1290° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 1290° can be given in terms of other trigonometric functions as:

sin(1290°)/cos(1290°)
± sin 1290°/√(1 - sin²(1290°))
± √(1 - cos²(1290°))/cos 1290°
± 1/√(cosec²(1290°) - 1)
± √(sec²(1290°) - 1)
1/cot 1290°

☛ Also check: trigonometry table

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