Cot 105 Tan 15

Cot 105 Tan 15.

Cot 15 Degrees

The value of
cot xv degrees is 3.7320508. . .. Cot xv degrees in radians is written as cot (15° × π/180°), i.e., cot (π/12) or cot (0.261799. . .). In this commodity, we volition discuss the methods to detect the value of cot 15 degrees with examples.

  • Cot xv°:
    2 + √3
  • Cot 15° in decimal:
    3.7320508. . .
  • Cot (-fifteen degrees):
    -3.7320508. . . or -(2 + √iii)
  • Cot 15° in radians:

    cot (π/12) or cot (0.2617993 . . .)

What is the Value of Cot fifteen Degrees?

The value of cot 15 degrees in decimal is 3.732050807. . .. Cot fifteen degrees tin besides be expressed using the equivalent of the given angle (15 degrees) in radians (0.26179 . . .)

Nosotros know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 15 degrees = 15° × (π/180°) rad = π/12 or 0.2617 . . .
∴ cot 15° = cot(0.2617) = two + √3 or 3.7320508. . .

Explanation:

For cot fifteen degrees, the angle 15° lies between 0° and 90° (Commencement Quadrant). Since cotangent function is positive in the first quadrant, thus cot 15° value = 2 + √3 or 3.7320508. . .
Since the cotangent function is a periodic role, we can represent cot 15° as, cot 15 degrees = cot(15° + n × 180°), n ∈ Z.
⇒ cot 15° = cot 195° = cot 375°, then on.
Note:
Since, cotangent is an odd function, the value of cot(-15°) = -cot(15°).

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Methods to Find Value of Cot xv Degrees

The cotangent function is positive in the 1st quadrant. The value of cot xv° is given as 3.73205. . . We tin can find the value of cot xv degrees past:

  • Using Trigonometric Functions
  • Using Unit Circle

Cot 15° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot xv degrees as:

  • cos(fifteen°)/sin(15°)
  • ± cos 15°/√(i – cos²(15°))
  • ± √(1 – sin²(15°))/sin fifteen°
  • ± 1/√(sec²(15°) – 1)
  • ± √(cosec²(15°) – 1)
  • 1/tan fifteen°

Annotation: Since 15° lies in the 1st Quadrant, the final value of cot xv° volition exist positive.

We can employ trigonometric identities to stand for cot fifteen° as,

  • tan (90° – fifteen°) = tan 75°
  • -tan (90° + 15°) = -tan 105°
  • -cot (180° – 15°) = -cot 165°

Cot 15 Degrees Using Unit Circle

Value of cot 15

To find the value of cot xv degrees using the unit of measurement circle:

  • Rotate ‘r’ anticlockwise to form 15° bending with the positive x-axis.
  • The cot of 15 degrees equals the x-coordinate(0.9659) divided past y-coordinate(0.2588) of the point of intersection (0.9659, 0.2588) of unit circle and r.

Hence the value of cot xv° = x/y = 3.7321 (approx).

☛ Also Check:

  • cot 13 degrees
  • cot 390 degrees
  • cot 35 degrees
  • cot 30 degrees
  • cot 135 degrees
  • cot lxx degrees

FAQs on Cot 15 Degrees

What is Cot 15 Degrees?

Cot xv degrees is the value of cotangent trigonometric function for an bending equal to 15 degrees.


The value of cot 15° is 2 + √3 or 3.7321 (approx).

What is the Value of Cot fifteen Degrees in Terms of Sin xv°?

Using trigonometric identities, we tin write cot 15° in terms of sin 15° as, cot(15°) = √(i – sin²(xv°))/sin 15° . Hither, the value of sin xv° is equal to (√half-dozen – √ii)/4.

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How to Find Cot 15° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 15° tin can be given in terms of other trigonometric functions as:

  • cos(fifteen°)/sin(15°)
  • ± cos fifteen°/√(1 – cos²(15°))
  • ± √(one – sin²(fifteen°))/sin 15°
  • ± 1/√(sec²(15°) – 1)
  • ± √(cosec²(15°) – i)
  • 1/tan fifteen°

☛ Also cheque: trigonometric table

How to Notice the Value of Cot xv Degrees?

The value of cot 15 degrees can exist calculated by constructing an angle of fifteen° with the x-centrality, then finding the coordinates of the corresponding point (0.9659, 0.2588) on the unit circle. The value of cot xv° is equal to the x-coordinate(0.9659) divided by the y-coordinate (0.2588). ∴ cot 15° = 3.7321

What is the Verbal Value of Cot xv Degrees?

The
verbal value of cot xv degrees
can be given accurately up to 8 decimal places every bit three.73205080 or as ii + √3.

Cot 105 Tan 15

Source: https://www.cuemath.com/trigonometry/cot-15-degrees/

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