Tan 855 Degrees

The value of tan 855 degrees is -1. Tan 855 degrees in radians is written as tan (855° × π/180°), i.e., tan (19π/4) or tan (14.922565. . .). In this article, we will discuss the methods to find the value of tan 855 degrees with examples.

• Tan 855°: -1
• Tan (-855 degrees): 1
• Tan 855° in radians: tan (19π/4) or tan (14.9225651 . . .)

What is the Value of Tan 855 Degrees?

The value of tan 855 degrees is -1. Tan 855 degrees can also be expressed using the equivalent of the given angle (855 degrees) in radians (14.92256 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 855 degrees = 855° × (π/180°) rad = 19π/4 or 14.9225 . . .
∴ tan 855° = tan(14.9225) = -1

Explanation:

For tan 855°, the angle 855° > 360°. We can represent tan 855° as, tan(855° mod 360°) = tan(135°). The angle 855°, coterminal to angle 135°, is located in the Second Quadrant(Quadrant II).
Since tangent function is negative in the 2nd quadrant, thus tan 855 degrees value = -1
Similarly, given the periodic property of tan 855°, it can also be written as, tan 855 degrees = (855° + n × 180°), n ∈ Z.
⇒ tan 855° = tan 1035° = tan 1215°, and so on.
Note: Since, tangent is an odd function, the value of tan(-855°) = -tan(855°).

Methods to Find Value of Tan 855 Degrees

The tangent function is negative in the 2nd quadrant. The value of tan 855° is given as -1. We can find the value of tan 855 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 855 Degrees Using Unit Circle

To find the value of tan 855 degrees using the unit circle, represent 855° in the form (2 × 360°) + 135° [∵ 855°>360°] ∵ The angle 855° is coterminal to 135° angle and also tangent is a periodic function, tan 855° = tan 135°.

• Rotate ‘r’ anticlockwise to form 135° or 855° angle with the positive x-axis.
• The tan of 855 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 855° = y/x = -1

Tan 855° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 855 degrees as:

• sin(855°)/cos(855°)
• ± sin 855°/√(1 - sin²(855°))
• ± √(1 - cos²(855°))/cos 855°
• ± 1/√(cosec²(855°) - 1)
• ± √(sec²(855°) - 1)
• 1/cot 855°

Note: Since 855° lies in the 2nd Quadrant, the final value of tan 855° will be negative.

We can use trigonometric identities to represent tan 855° as,

• cot(90° - 855°) = cot(-765°)
• -cot(90° + 855°) = -cot 945°
• -tan (180° - 855°) = -tan(-675°)

☛ Also Check:

• tan 30 degrees
• tan 12 degrees
• tan 40 degrees
• tan 23 degrees
• tan 145 degrees
• tan 405 degrees

FAQs on Tan 855 Degrees

What is Tan 855 Degrees?

Tan 855 degrees is the value of tangent trigonometric function for an angle equal to 855 degrees. The value of tan 855° is -1.

What is the Value of Tan 855° in Terms of Cosec 855°?

Since the tangent function can be represented using the cosecant function, we can write tan 855° as -1/√(cosec²(855°) - 1). The value of cosec 855° is equal to 1.41421.

How to Find Tan 855° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 855° can be given in terms of other trigonometric functions as:

• sin(855°)/cos(855°)
• ± sin 855°/√(1 - sin²(855°))
• ± √(1 - cos²(855°))/cos 855°
• ± 1/√(cosec²(855°) - 1)
• ± √(sec²(855°) - 1)
• 1/cot 855°

☛ Also check: trigonometric table

How to Find the Value of Tan 855 Degrees?

The value of tan 855 degrees can be calculated by constructing an angle of 855° 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 855° is equal to the y-coordinate(0.7071) divided by the x-coordinate (-0.7071). ∴ tan 855° = -1

What is the Value of Tan 855 Degrees in Terms of Cot 855°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 855° as 1/cot(855°). The value of cot 855° is equal to -1.