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Tan 130 Degrees

The value of tan 130 degrees is -1.1917535. . .. Tan 130 degrees in radians is written as tan (130° × π/180°), i.e., tan (13π/18) or tan (2.268928. . .). In this article, we will discuss the methods to find the value of tan 130 degrees with examples.

Tan 130° in decimal: -1.1917535. . .
Tan (-130 degrees): 1.1917535. . .
Tan 130° in radians: tan (13π/18) or tan (2.2689280 . . .)

What is the Value of Tan 130 Degrees?

The value of tan 130 degrees in decimal is -1.191753592. . .. Tan 130 degrees can also be expressed using the equivalent of the given angle (130 degrees) in radians (2.26892 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 130 degrees = 130° × (π/180°) rad = 13π/18 or 2.2689 . . .
∴ tan 130° = tan(2.2689) = -1.1917535. . .

Explanation:

For tan 130 degrees, the angle 130° lies between 90° and 180° (Second Quadrant). Since tangent function is negative in the second quadrant, thus tan 130° value = -1.1917535. . .
Since the tangent function is a periodic function, we can represent tan 130° as, tan 130 degrees = tan(130° + n × 180°), n ∈ Z.
⇒ tan 130° = tan 310° = tan 490°, and so on.
Note: Since, tangent is an odd function, the value of tan(-130°) = -tan(130°).

Methods to Find Value of Tan 130 Degrees

The tangent function is negative in the 2nd quadrant. The value of tan 130° is given as -1.19175. . .. We can find the value of tan 130 degrees by:

Using Unit Circle
Using Trigonometric Functions

Tan 130 Degrees Using Unit Circle

To find the value of tan 130 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 130° angle with the positive x-axis.
The tan of 130 degrees equals the y-coordinate(0.766) divided by x-coordinate(-0.6428) of the point of intersection (-0.6428, 0.766) of unit circle and r.

Hence the value of tan 130° = y/x = -1.1918 (approx).

Tan 130° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 130 degrees as:

sin(130°)/cos(130°)
± sin 130°/√(1 - sin²(130°))
± √(1 - cos²(130°))/cos 130°
± 1/√(cosec²(130°) - 1)
± √(sec²(130°) - 1)
1/cot 130°

Note: Since 130° lies in the 2nd Quadrant, the final value of tan 130° will be negative.

We can use trigonometric identities to represent tan 130° as,

cot(90° - 130°) = cot(-40°)
-cot(90° + 130°) = -cot 220°
-tan (180° - 130°) = -tan 50°

☛ Also Check:

Examples Using Tan 130 Degrees

Example 1: Find the value of (2 sin (65°) cos (65°) sec (130°)). [Hint: Use tan 130° = -1.1918]

Solution:

Using sin 2a formula,
2 sin (65°) cos (65°) = sin (2 × 65°) = sin 130°
⇒ 2 sin (65°) cos (65°) sec(130°) = sin 130° sec 130°
= sin 130°/cos 130° = tan 130°
⇒ (2 sin (65°) cos (65°) sec(130°)) = -1.1918
Example 2: Simplify: 3 (tan 130°/cot(-40°))

Solution:

We know tan 130° = cot(-40°)
⇒ 3 tan 130°/cot(-40°) = 3 (tan 130°/tan 130°)
= 3(1) = 3
Example 3: Using the value of tan 130°, solve: (sec²(130°) - 1).

Solution:
We know, (sec²(130°) - 1) = (tan²(130°)) = 1.4203
⇒ (sec²(130°) - 1) = 1.4203

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FAQs on Tan 130 Degrees

What is Tan 130 Degrees?

Tan 130 degrees is the value of tangent trigonometric function for an angle equal to 130 degrees. The value of tan 130° is -1.1918 (approx).

How to Find Tan 130° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 130° can be given in terms of other trigonometric functions as:

sin(130°)/cos(130°)
± sin 130°/√(1 - sin²(130°))
± √(1 - cos²(130°))/cos 130°
± 1/√(cosec²(130°) - 1)
± √(sec²(130°) - 1)
1/cot 130°

☛ Also check: trigonometry table

How to Find the Value of Tan 130 Degrees?

The value of tan 130 degrees can be calculated by constructing an angle of 130° with the x-axis, and then finding the coordinates of the corresponding point (-0.6428, 0.766) on the unit circle. The value of tan 130° is equal to the y-coordinate(0.766) divided by the x-coordinate (-0.6428). ∴ tan 130° = -1.1918

What is the Value of Tan 130 Degrees in Terms of Cot 130°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 130° as 1/cot(130°). The value of cot 130° is equal to -0.83909.

What is the Value of Tan 130° in Terms of Cosec 130°?

Since the tangent function can be represented using the cosecant function, we can write tan 130° as -1/√(cosec²(130°) - 1). The value of cosec 130° is equal to 1.30540.

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