Cot 105 Degrees
The value of cot 105 degrees is -0.2679491. . .. Cot 105 degrees in radians is written as cot (105° × π/180°), i.e., cot (7π/12) or cot (1.832595. . .). In this article, we will discuss the methods to find the value of cot 105 degrees with examples.
- Cot 105°: -2 + √3
- Cot 105° in decimal: -0.2679491. . .
- Cot (-105 degrees): 0.2679491. . . or 2 - √3
- Cot 105° in radians: cot (7π/12) or cot (1.8325957 . . .)
What is the Value of Cot 105 Degrees?
The value of cot 105 degrees in decimal is -0.267949192. . .. Cot 105 degrees can also be expressed using the equivalent of the given angle (105 degrees) in radians (1.83259 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 105 degrees = 105° × (π/180°) rad = 7π/12 or 1.8325 . . .
∴ cot 105° = cot(1.8325) = -2 + √3 or -0.2679491. . .
Explanation:
For cot 105 degrees, the angle 105° lies between 90° and 180° (Second Quadrant). Since cotangent function is negative in the second quadrant, thus cot 105° value = -2 + √3 or -0.2679491. . .
Since the cotangent function is a periodic function, we can represent cot 105° as, cot 105 degrees = cot(105° + n × 180°), n ∈ Z.
⇒ cot 105° = cot 285° = cot 465°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-105°) = -cot(105°).
Methods to Find Value of Cot 105 Degrees
The cotangent function is negative in the 2nd quadrant. The value of cot 105° is given as -0.26794. . . We can find the value of cot 105 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Cot 105 Degrees Using Unit Circle
To find the value of cot 105 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 105° angle with the positive x-axis.
- The cot of 105 degrees equals the x-coordinate(-0.2588) divided by y-coordinate(0.9659) of the point of intersection (-0.2588, 0.9659) of unit circle and r.
Hence the value of cot 105° = x/y = -0.2679 (approx).
Cot 105° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 105 degrees as:
- cos(105°)/sin(105°)
- ± cos 105°/√(1 - cos²(105°))
- ± √(1 - sin²(105°))/sin 105°
- ± 1/√(sec²(105°) - 1)
- ± √(cosec²(105°) - 1)
- 1/tan 105°
Note: Since 105° lies in the 2nd Quadrant, the final value of cot 105° will be negative.
We can use trigonometric identities to represent cot 105° as,
- tan (90° - 105°) = tan(-15°)
- -tan (90° + 105°) = -tan 195°
- -cot (180° - 105°) = -cot 75°
☛ Also Check:
FAQs on Cot 105 Degrees
What is Cot 105 Degrees?
Cot 105 degrees is the value of cotangent trigonometric function for an angle equal to 105 degrees. The value of cot 105° is -2 + √3 or -0.2679 (approx).
How to Find Cot 105° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 105° can be given in terms of other trigonometric functions as:
- cos(105°)/sin(105°)
- ± cos 105°/√(1 - cos²(105°))
- ± √(1 - sin²(105°))/sin 105°
- ± 1/√(sec²(105°) - 1)
- ± √(cosec²(105°) - 1)
- 1/tan 105°
☛ Also check: trigonometry table
What is the Value of Cot 105 Degrees in Terms of Cos 105°?
We know, using trig identities, we can write cot 105° as cos 105°/√(1 - cos²(105°)). Here, the value of cos 105° is equal to -0.258819.
How to Find the Value of Cot 105 Degrees?
The value of cot 105 degrees can be calculated by constructing an angle of 105° with the x-axis, and then finding the coordinates of the corresponding point (-0.2588, 0.9659) on the unit circle. The value of cot 105° is equal to the x-coordinate(-0.2588) divided by the y-coordinate (0.9659). ∴ cot 105° = -0.2679
What is the Exact Value of Cot 105 Degrees?
The exact value of cot 105 degrees can be given accurately up to 8 decimal places as -0.26794919 or as -2 + √3.