Tan 900 Degrees

The value of tan 900 degrees is 0. Tan 900 degrees in radians is written as tan (900° × π/180°), i.e., tan (5π) or tan (15.707963. . .). In this article, we will discuss the methods to find the value of tan 900 degrees with examples.

• Tan 900°: 0
• Tan (-900 degrees): 0
• Tan 900° in radians: tan (5π) or tan (15.7079632 . . .)

What is the Value of Tan 900 Degrees?

The value of tan 900 degrees is 0. Tan 900 degrees can also be expressed using the equivalent of the given angle (900 degrees) in radians (15.70796 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 900 degrees = 900° × (π/180°) rad = 5π or 15.7079 . . .
∴ tan 900° = tan(15.7079) = 0

Explanation:

For tan 900°, the angle 900° > 360°. We can represent tan 900° as, tan(900° mod 360°) = tan(180°). The angle 900°, coterminal to angle 180°, lies on the negative x-axis.
Thus, tan 900 degrees value = 0
Similarly, given the periodic property of tan 900°, it can also be written as, tan 900 degrees = (900° + n × 180°), n ∈ Z.
⇒ tan 900° = tan 1080° = tan 1260°, and so on.
Note: Since, tangent is an odd function, the value of tan(-900°) = -tan(900°) = 0.

Methods to Find Value of Tan 900 Degrees

The value of tan 900° is given as 0. We can find the value of tan 900 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 900 Degrees Using Unit Circle

To find the value of tan 900 degrees using the unit circle, represent 900° in the form (2 × 360°) + 180° [∵ 900°>360°] ∵ The angle 900° is coterminal to 180° angle and also tangent is a periodic function, tan 900° = tan 180°.

• Rotate ‘r’ anticlockwise to form 180° or 900° angle with the positive x-axis.
• The tan of 900 degrees equals the y-coordinate(0) divided by x-coordinate(-1) of the point of intersection (-1, 0) of unit circle and r.

Hence the value of tan 900° = y/x = 0

Tan 900° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 900 degrees as:

• sin(900°)/cos(900°)
• ± sin 900°/√(1 - sin²(900°))
• ± √(1 - cos²(900°))/cos 900°
• ± 1/√(cosec²(900°) - 1)
• ± √(sec²(900°) - 1)
• 1/cot 900°

Note: Since 900° lies on the negative x-axis, the final value of tan 900° is 0.

We can use trigonometric identities to represent tan 900° as,

• cot(90° - 900°) = cot(-810°)
• -cot(90° + 900°) = -cot 990°
• -tan (180° - 900°) = -tan(-720°)

☛ Also Check:

• tan 75 degrees
• tan 50 degrees
• tan 45 degrees
• tan 56 degrees
• tan 900 degrees
• tan 65 degrees

FAQs on Tan 900 Degrees

What is Tan 900 Degrees?

Tan 900 degrees is the value of tangent trigonometric function for an angle equal to 900 degrees. The value of tan 900° is 0.

What is the Value of Tan 900 Degrees in Terms of Cot 900°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 900° as 1/cot(900°). 

What is the Exact Value of tan 900 Degrees?

The exact value of tan 900 degrees is 0.

How to Find the Value of Tan 900 Degrees?

The value of tan 900 degrees can be calculated by constructing an angle of 900° with the x-axis, and then finding the coordinates of the corresponding point (-1, 0) on the unit circle. The value of tan 900° is equal to the y-coordinate(0) divided by the x-coordinate (-1). ∴ tan 900° = 0

How to Find Tan 900° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 900° can be given in terms of other trigonometric functions as:

• sin(900°)/cos(900°)
• ± sin 900°/√(1 - sin²(900°))
• ± √(1 - cos²(900°))/cos 900°
• ± 1/√(cosec²(900°) - 1)
• ± √(sec²(900°) - 1)
• 1/cot 900°

☛ Also check: trigonometry table