Tan 135 Degrees

The value of tan 135 degrees is -1. Tan 135 degrees in radians is written as tan (135° × π/180°), i.e., tan (3π/4) or tan (2.356194. . .). In this article, we will discuss the methods to find the value of tan 135 degrees with examples.

• Tan 135°: -1
• Tan (-135 degrees): 1
• Tan 135° in radians: tan (3π/4) or tan (2.3561944 . . .)

What is the Value of Tan 135 Degrees?

The value of tan 135 degrees is -1. Tan 135 degrees can also be expressed using the equivalent of the given angle (135 degrees) in radians (2.35619 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 135 degrees = 135° × (π/180°) rad = 3π/4 or 2.3561 . . .
∴ tan 135° = tan(2.3561) = -1

Explanation:

For tan 135 degrees, the angle 135° lies between 90° and 180° (Second Quadrant). Since tangent function is negative in the second quadrant, thus tan 135° value = -1
Since the tangent function is a periodic function, we can represent tan 135° as, tan 135 degrees = tan(135° + n × 180°), n ∈ Z.
⇒ tan 135° = tan 315° = tan 495°, and so on.
Note: Since, tangent is an odd function, the value of tan(-135°) = -tan(135°).

Methods to Find Value of Tan 135 Degrees

The tangent function is negative in the 2nd quadrant. The value of tan 135° is given as -1. We can find the value of tan 135 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 135 Degrees Using Unit Circle

To find the value of tan 135 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 135° angle with the positive x-axis.
• The tan of 135 degrees equals the y-coordinate(0.7071) divided by x-coordinate(-0.7071) of the point of intersection (-0.7071, 0.7071) of unit circle and r.

Hence the value of tan 135° = y/x = -1

Tan 135° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 135 degrees as:

• sin(135°)/cos(135°)
• ± sin 135°/√(1 - sin²(135°))
• ± √(1 - cos²(135°))/cos 135°
• ± 1/√(cosec²(135°) - 1)
• ± √(sec²(135°) - 1)
• 1/cot 135°

Note: Since 135° lies in the 2nd Quadrant, the final value of tan 135° will be negative.

We can use trigonometric identities to represent tan 135° as,

• cot(90° - 135°) = cot(-45°)
• -cot(90° + 135°) = -cot 225°
• -tan (180° - 135°) = -tan 45°

☛ Also Check:

• tan 360 degrees
• tan 690 degrees
• tan 270 degrees
• tan 1290 degrees
• tan 34 degrees
• tan 78 degrees

FAQs on Tan 135 Degrees

What is Tan 135 Degrees?

Tan 135 degrees is the value of tangent trigonometric function for an angle equal to 135 degrees. The value of tan 135° is -1.

How to Find the Value of Tan 135 Degrees?

The value of tan 135 degrees can be calculated by constructing an angle of 135° with the x-axis, and then finding the coordinates of the corresponding point (-0.7071, 0.7071) on the unit circle. The value of tan 135° is equal to the y-coordinate(0.7071) divided by the x-coordinate (-0.7071). ∴ tan 135° = -1

How to Find Tan 135° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 135° can be given in terms of other trigonometric functions as:

• sin(135°)/cos(135°)
• ± sin 135°/√(1 - sin²(135°))
• ± √(1 - cos²(135°))/cos 135°
• ± 1/√(cosec²(135°) - 1)
• ± √(sec²(135°) - 1)
• 1/cot 135°

☛ Also check: trigonometry table

What is the Value of Tan 135 Degrees in Terms of Cos 135°?

We know, using trig identities, we can write tan 135° as √(1 - cos²(135°))/cos 135°. Here, the value of cos 135° is equal to -0.707106.

What is the Value of Tan 135° in Terms of Cosec 135°?

Since the tangent function can be represented using the cosecant function, we can write tan 135° as -1/√(cosec²(135°) - 1). The value of cosec 135° is equal to 1.41421.