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 x-axis.
• The cot of 7pi/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 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:

• tan pi/8
• sin pi/8
• tan pi/3
• tan 3pi/4
• sin 11pi/12
• cos 2pi/7

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 x-axis, 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 x-coordinate(0.7071) divided by the y-coordinate (-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.