Cot 15pi/4

The value of cot 15pi/4 is -1. Cot 15pi/4 radians in degrees is written as cot ((15π/4) × 180°/π), i.e., cot (675°). In this article, we will discuss the methods to find the value of cot 15pi/4 with examples.

• Cot 15pi/4: -1
• Cot (-15pi/4): 1
• Cot 15pi/4 in degrees: cot (675°)

What is the Value of Cot 15pi/4?

The value of cot 15pi/4 is -1. Cot 15pi/4 can also be expressed using the equivalent of the given angle (15pi/4) in degrees (675°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 15pi/4 radians = 15pi/4 × (180°/pi) = 675° or 675 degrees
∴ cot 15pi/4 = cot 15π/4 = cot(675°) = -1

Explanation:

For cot 15pi/4, the angle 15pi/4 > 2pi. We can represent cot 15pi/4 as, cot(15pi/4 mod 2pi) = cot(7pi/4). The angle 15pi/4, coterminal to angle 7pi/4, is located in the Fourth Quadrant(Quadrant IV).
Since cot function is negative in the 4th quadrant, thus cot 15pi/4 value = -1
Similarly, given the periodic property of cot 15pi/4, it can also be written as, cot 15pi/4 = (15pi/4 + n × pi), n ∈ Z.
⇒ cot 15pi/4 = cot 19pi/4 = cot 23pi/4, and so on.
Note: Since, cotangent is an odd function, the value of cot(-15pi/4) = -cot(15pi/4).

Methods to Find Value of Cot 15pi/4

The cotangent function is negative in the 4th quadrant. The value of cot 15pi/4 is given as -1. We can find the value of cot 15pi/4 by:

• Using Unit Circle
• Using Trigonometric Functions

Cot 15pi/4 Using Unit Circle

To find the value of cot 15pi/4 using the unit circle, represent 15pi/4 in the form (1 × 2pi) + 7pi/4 [∵ 15pi/4>2pi] ∵ The angle 15pi/4 is coterminal to 7pi/4 angle and also cotangent is a periodic function, cot 15pi/4 = cot 7pi/4.

• Rotate ‘r’ anticlockwise to form 7pi/4 or 15pi/4 angle with the positive x-axis.
• The cot of 15pi/4 equals the x-coordinate(0.7071) divided by y-coordinate(-0.7071) of the point of intersection (0.7071, -0.7071) of unit circle and r.

Hence the value of cot 15pi/4 = x/y = -1

Cot 15pi/4 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 15pi/4 as:

• cos(15pi/4)/sin(15pi/4)
• ± cos(15pi/4)/√(1 - cos²(15pi/4))
• ± √(1 - sin²(15pi/4))/sin(15pi/4)
• ± 1/√(sec²(15pi/4) - 1)
• ± √(cosec²(15pi/4) - 1)
• 1/tan(15pi/4)

Note: Since 15pi/4 lies in the 4th Quadrant, the final value of cot 15pi/4 will be negative.

We can use trigonometric identities to represent cot 15pi/4 as,

• tan (pi/2 - 15pi/4) = tan(-13pi/4)
• -tan (pi/2 + 15pi/4) = -tan 17pi/4
• -cot (pi - 15pi/4) = -cot(-11pi/4)

☛ Also Check:

• tan pi/3
• cos 5pi/4
• sec 3pi
• sec 7pi/4
• sec pi/4
• tan pi/4

FAQs on Cot 15pi/4

What is Cot 15pi/4?

Cot 15pi/4 is the value of cotangent trigonometric function for an angle equal to 15π/4 radians. The value of cot 15pi/4 is -1.

What is the Value of Cot 15pi/4 in Terms of Tan 15pi/4?

Since the cotangent function is the reciprocal of the tangent function, we can write cot 15pi/4 as 1/tan(15pi/4). The value of tan 15pi/4 is equal to -1.

How to Find the Value of Cot 15pi/4?

The value of cot 15pi/4 can be calculated by constructing an angle of 15π/4 radians with the x-axis, and then finding the coordinates of the corresponding point (0.7071, -0.7071) on the unit circle. The value of cot 15pi/4 is equal to the x-coordinate(0.7071) divided by the y-coordinate (-0.7071). ∴ cot 15pi/4 = -1

What is the Value of Cot 15pi/4 in Terms of Cosec 15pi/4?

Since the cotangent function can be represented using the cosecant function, we can write cot 15pi/4 as -√(cosec²(15pi/4) - 1). The value of cosec 15pi/4 is equal to -1.41421.

How to Find Cot 15pi/4 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 15pi/4 can be given in terms of other trigonometric functions as:

• cos(15pi/4)/sin(15pi/4)
• ± cos(15pi/4)/√(1 - cos²(15pi/4))
• ± √(1 - sin²(15pi/4))/sin(15pi/4)
• ± 1/√(sec²(15pi/4) - 1)
• ± √(cosec²(15pi/4) - 1)
• 1/tan(15pi/4)

☛ Also check: trigonometry table