# 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 (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 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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