Cot 7pi/4
The value of cot 7pi/4 is 1. Cot 7pi/4 radians in degrees is written as cot ((7π/4) × 180°/π), i.e., cot (315°). In this article, we will discuss the methods to find the value of cot 7pi/4 with examples.
 Cot 7pi/4: 1
 Cot (7pi/4): 1
 Cot 7pi/4 in degrees: cot (315°)
What is the Value of Cot 7pi/4?
The value of cot 7pi/4 is 1. Cot 7pi/4 can also be expressed using the equivalent of the given angle (7pi/4) in degrees (315°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi/4 radians = 7pi/4 × (180°/pi) = 315° or 315 degrees
∴ cot 7pi/4 = cot 7π/4 = cot(315°) = 1
Explanation:
For cot 7pi/4, the angle 7pi/4 lies between 3pi/2 and 2pi (Fourth Quadrant). Since cotangent function is negative in the fourth quadrant, thus cot 7pi/4 value = 1
Since the cotangent function is a periodic function, we can represent cot 7pi/4 as, cot 7pi/4 = cot(7pi/4 + n × pi), n ∈ Z.
⇒ cot 7pi/4 = cot 11pi/4 = cot 15pi/4 , and so on.
Note: Since, cotangent is an odd function, the value of cot(7pi/4) = cot(7pi/4).
Methods to Find Value of Cot 7pi/4
The cotangent function is negative in the 4th quadrant. The value of cot 7pi/4 is given as 1. We can find the value of cot 7pi/4 by:
 Using Unit Circle
 Using Trigonometric Functions
Cot 7pi/4 Using Unit Circle
To find the value of cot 7π/4 using the unit circle:
 Rotate ‘r’ anticlockwise to form 7pi/4 angle with the positive xaxis.
 The cot of 7pi/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 7pi/4 = x/y = 1
Cot 7pi/4 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot 7pi/4 as:
 cos(7pi/4)/sin(7pi/4)
 ± cos(7pi/4)/√(1  cos²(7pi/4))
 ± √(1  sin²(7pi/4))/sin(7pi/4)
 ± 1/√(sec²(7pi/4)  1)
 ± √(cosec²(7pi/4)  1)
 1/tan(7pi/4)
Note: Since 7pi/4 lies in the 4th Quadrant, the final value of cot 7pi/4 will be negative.
We can use trigonometric identities to represent cot 7pi/4 as,
 tan (pi/2  7pi/4) = tan(5pi/4)
 tan (pi/2 + 7pi/4) = tan 9pi/4
 cot (pi  7pi/4) = cot(3pi/4)
☛ Also Check:
Examples Using Cot 7pi/4

Example 1: Using the value of cot 7pi/4, solve: (cosec²(7pi/4)  1).
Solution:
We know, (cosec²(7pi/4)  1) = (cot²(7pi/4)) = 1
⇒ (cosec²(7pi/4)  1) = 1 
Example 2: Find the value of 7 cot(7pi/4)/10 cot(3pi/4).
Solution:
Using trigonometric identities, we know, cot(7pi/4) = cot(pi  7pi/4) = cot(3pi/4).
⇒ cot(7pi/4) = cot(3pi/4)
⇒ Value of 7 cot(7pi/4)/10 cot(3pi/4) = 7/10 
Example 3: Find the value of cot 7pi/4 if tan 7pi/4 is 1.
Solution:
Since, cot 7pi/4 = 1/tan(7pi/4)
⇒ cot 7pi/4 = 1/(1) = 1
FAQs on Cot 7pi/4
What is Cot 7pi/4?
Cot 7pi/4 is the value of cotangent trigonometric function for an angle equal to 7π/4 radians. The value of cot 7pi/4 is 1.
How to Find the Value of Cot 7pi/4?
The value of cot 7pi/4 can be calculated by constructing an angle of 7π/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 7pi/4 is equal to the xcoordinate(0.7071) divided by the ycoordinate (0.7071). ∴ cot 7pi/4 = 1
How to Find Cot 7pi/4 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot 7pi/4 can be given in terms of other trigonometric functions as:
 cos(7pi/4)/sin(7pi/4)
 ± cos(7pi/4)/√(1  cos²(7pi/4))
 ± √(1  sin²(7pi/4))/sin(7pi/4)
 ± 1/√(sec²(7pi/4)  1)
 ± √(cosec²(7pi/4)  1)
 1/tan(7pi/4)
☛ Also check: trigonometric table
What is the Value of Cot 7pi/4 in Terms of Sec 7pi/4?
We can represent the cotangent function in terms of the secant function using trig identities, cot 7pi/4 can be written as 1/√(sec²(7pi/4)  1). Here, the value of sec 7pi/4 is equal to 1.4142.
What is the Value of Cot 7pi/4 in Terms of Cos 7pi/4?
We know, using trig identities, we can write cot 7pi/4 as cos(7pi/4)/√(1  cos²(7pi/4)). Here, the value of cos 7pi/4 is equal to 0.707106.
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