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Tan 125 Degrees

The value of tan 125 degrees is -1.4281480. . .. Tan 125 degrees in radians is written as tan (125° × π/180°), i.e., tan (25π/36) or tan (2.181661. . .). In this article, we will discuss the methods to find the value of tan 125 degrees with examples.

Tan 125° in decimal: -1.4281480. . .
Tan (-125 degrees): 1.4281480. . .
Tan 125° in radians: tan (25π/36) or tan (2.1816615 . . .)

What is the Value of Tan 125 Degrees?

The value of tan 125 degrees in decimal is -1.428148006. . .. Tan 125 degrees can also be expressed using the equivalent of the given angle (125 degrees) in radians (2.18166 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 125 degrees = 125° × (π/180°) rad = 25π/36 or 2.1816 . . .
∴ tan 125° = tan(2.1816) = -1.4281480. . .

Explanation:

For tan 125 degrees, the angle 125° lies between 90° and 180° (Second Quadrant). Since tangent function is negative in the second quadrant, thus tan 125° value = -1.4281480. . .
Since the tangent function is a periodic function, we can represent tan 125° as, tan 125 degrees = tan(125° + n × 180°), n ∈ Z.
⇒ tan 125° = tan 305° = tan 485°, and so on.
Note: Since, tangent is an odd function, the value of tan(-125°) = -tan(125°).

Methods to Find Value of Tan 125 Degrees

The tangent function is negative in the 2nd quadrant. The value of tan 125° is given as -1.42814. . .. We can find the value of tan 125 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 125° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 125 degrees as:

sin(125°)/cos(125°)
± sin 125°/√(1 - sin²(125°))
± √(1 - cos²(125°))/cos 125°
± 1/√(cosec²(125°) - 1)
± √(sec²(125°) - 1)
1/cot 125°

Note: Since 125° lies in the 2nd Quadrant, the final value of tan 125° will be negative.

We can use trigonometric identities to represent tan 125° as,

cot(90° - 125°) = cot(-35°)
-cot(90° + 125°) = -cot 215°
-tan (180° - 125°) = -tan 55°

Tan 125 Degrees Using Unit Circle

To find the value of tan 125 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 125° angle with the positive x-axis.
The tan of 125 degrees equals the y-coordinate(0.8192) divided by x-coordinate(-0.5736) of the point of intersection (-0.5736, 0.8192) of unit circle and r.

Hence the value of tan 125° = y/x = -1.4281 (approx).

☛ Also Check:

Examples Using Tan 125 Degrees

Example 1: Simplify: 7 (tan 125°/cot(-35°))

Solution:

We know tan 125° = cot(-35°)
⇒ 7 tan 125°/cot(-35°) = 7 (tan 125°/tan 125°)
= 7(1) = 7
Example 2: Find the value of (2 sin (62.5°) cos (62.5°) sec (125°)). [Hint: Use tan 125° = -1.4281]

Solution:

Using sin 2a formula,
2 sin (62.5°) cos (62.5°) = sin (2 × 62.5°) = sin 125°
⇒ 2 sin (62.5°) cos (62.5°) sec(125°) = sin 125° sec 125°
= sin 125°/cos 125° = tan 125°
⇒ (2 sin (62.5°) cos (62.5°) sec(125°)) = -1.4281
Example 3: Using the value of tan 125°, solve: (sec²(125°) - 1).

Solution:
We know, (sec²(125°) - 1) = (tan²(125°)) = 2.0396
⇒ (sec²(125°) - 1) = 2.0396

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FAQs on Tan 125 Degrees

What is Tan 125 Degrees?

Tan 125 degrees is the value of tangent trigonometric function for an angle equal to 125 degrees. The value of tan 125° is -1.4281 (approx).

What is the Value of Tan 125 Degrees in Terms of Sin 125°?

Using trigonometric identities, we can write tan 125° in terms of sin 125° as, tan(125°) = -sin 125°/√(1 - sin²(125°)) . Here, the value of sin 125° is equal to 0.8192.

How to Find Tan 125° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 125° can be given in terms of other trigonometric functions as:

sin(125°)/cos(125°)
± sin 125°/√(1 - sin²(125°))
± √(1 - cos²(125°))/cos 125°
± 1/√(cosec²(125°) - 1)
± √(sec²(125°) - 1)
1/cot 125°

☛ Also check: trigonometry table

How to Find the Value of Tan 125 Degrees?

The value of tan 125 degrees can be calculated by constructing an angle of 125° with the x-axis, and then finding the coordinates of the corresponding point (-0.5736, 0.8192) on the unit circle. The value of tan 125° is equal to the y-coordinate(0.8192) divided by the x-coordinate (-0.5736). ∴ tan 125° = -1.4281

What is the Value of Tan 125° in Terms of Cosec 125°?

Since the tangent function can be represented using the cosecant function, we can write tan 125° as -1/√(cosec²(125°) - 1). The value of cosec 125° is equal to 1.22077.

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