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Cot 315 Degrees

The value of cot 315 degrees is -1. Cot 315 degrees in radians is written as cot (315° × π/180°), i.e., cot (7π/4) or cot (5.497787. . .). In this article, we will discuss the methods to find the value of cot 315 degrees with examples.

Cot 315°: -1
Cot (-315 degrees): 1
Cot 315° in radians: cot (7π/4) or cot (5.4977871 . . .)

What is the Value of Cot 315 Degrees?

The value of cot 315 degrees is -1. Cot 315 degrees can also be expressed using the equivalent of the given angle (315 degrees) in radians (5.49778 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 315 degrees = 315° × (π/180°) rad = 7π/4 or 5.4977 . . .
∴ cot 315° = cot(5.4977) = -1

Explanation:

For cot 315 degrees, the angle 315° lies between 270° and 360° (Fourth Quadrant). Since cotangent function is negative in the fourth quadrant, thus cot 315° value = -1
Since the cotangent function is a periodic function, we can represent cot 315° as, cot 315 degrees = cot(315° + n × 180°), n ∈ Z.
⇒ cot 315° = cot 495° = cot 675°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-315°) = -cot(315°).

Methods to Find Value of Cot 315 Degrees

The cotangent function is negative in the 4th quadrant. The value of cot 315° is given as -1. We can find the value of cot 315 degrees by:

Using Trigonometric Functions
Using Unit Circle

Cot 315° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 315 degrees as:

cos(315°)/sin(315°)
± cos 315°/√(1 - cos²(315°))
± √(1 - sin²(315°))/sin 315°
± 1/√(sec²(315°) - 1)
± √(cosec²(315°) - 1)
1/tan 315°

Note: Since 315° lies in the 4th Quadrant, the final value of cot 315° will be negative.

We can use trigonometric identities to represent cot 315° as,

tan (90° - 315°) = tan(-225°)
-tan (90° + 315°) = -tan 405°
-cot (180° - 315°) = -cot(-135°)

Cot 315 Degrees Using Unit Circle

To find the value of cot 315 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 315° angle with the positive x-axis.
The cot of 315 degrees 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 315° = x/y = -1

☛ Also Check:

Examples Using Cot 315 Degrees

Example 1: Find the value of 2 cot(315°)/9 cot(-135°).

Solution:

Using trigonometric identities, we know, cot(315°) = -cot(180° - 315°) = -cot(-135°).
⇒ cot(315°) = -cot(-135°)
⇒ Value of 2 cot(315°)/9 cot(-135°) = -2/9
Example 2: Using the value of cot 315°, solve: (cosec²(315°) - 1).

Solution:
We know, (cosec²(315°) - 1) = (cot²(315°)) = 1
⇒ (cosec²(315°) - 1) = 1
Example 3: Simplify: 3 (cot 315°/tan(-225°))

Solution:

We know cot 315° = tan(-225°)
⇒ 3 cot 315°/tan(-225°) = 3 (cot 315°/cot 315°)
= 3(1) = 3

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FAQs on Cot 315 Degrees

What is Cot 315 Degrees?

Cot 315 degrees is the value of cotangent trigonometric function for an angle equal to 315 degrees. The value of cot 315° is -1.

How to Find Cot 315° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 315° can be given in terms of other trigonometric functions as:

cos(315°)/sin(315°)
± cos 315°/√(1 - cos²(315°))
± √(1 - sin²(315°))/sin 315°
± 1/√(sec²(315°) - 1)
± √(cosec²(315°) - 1)
1/tan 315°

☛ Also check: trigonometric table

What is the Exact Value of Cot 315 Degrees?

The exact value of cot 315 degrees is -1.

What is the Value of Cot 315 Degrees in Terms of Sin 315°?

Using trigonometric identities, we can write cot 315° in terms of sin 315° as, cot(315°) = √(1 - sin²(315°))/sin 315° . Here, the value of sin 315° is equal to -(1/√2).

How to Find the Value of Cot 315 Degrees?

The value of cot 315 degrees can be calculated by constructing an angle of 315° 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 315° is equal to the x-coordinate(0.7071) divided by the y-coordinate (-0.7071). ∴ cot 315° = -1

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