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 xaxis.
 The cot of 15pi/4 equals the xcoordinate(0.7071) divided by ycoordinate(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:
Examples Using Cot 15pi/4

Example 1: Using the value of cot 15pi/4, solve: (cosec²(15pi/4)  1).
Solution:
We know, (cosec²(15pi/4)  1) = (cot²(15pi/4)) = 1
⇒ (cosec²(15pi/4)  1) = 1 
Example 2: Find the value of 4 cot(15pi/4)/8 cot(11pi/4).
Solution:
Using trigonometric identities, we know, cot(15pi/4) = cot(pi  15pi/4) = cot(11pi/4).
⇒ cot(15pi/4) = cot(11pi/4)
⇒ Value of 4 cot(15pi/4)/8 cot(11pi/4) = 4/8 = 1/2 
Example 3: Find the value of (cos (15pi/4) cosec (15pi/8) sec (15pi/8))/2. [Hint: Use cot 15pi/4 = 1]
Solution:
Using trigonometry formulas,
(cos (15pi/4) cosec (15pi/8) sec (15pi/8))/2 = cos (15pi/4)/(2 sin (15pi/8) cos (15pi/8))
Using sin 2a formula,
2 sin (15pi/8) cos (15pi/8) = sin (2 × 15pi/8) = sin 15pi/4
⇒ cos (15pi/4) / sin (15pi/4) = cot 15pi/4
⇒ (cos (15pi/4) cosec (15pi/8) sec (15pi/8))/2 = 1
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 xaxis, 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 xcoordinate(0.7071) divided by the ycoordinate (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
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