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Cot 50 Degrees

The value of cot 50 degrees is 0.8390996. . .. Cot 50 degrees in radians is written as cot (50° × π/180°), i.e., cot (5π/18) or cot (0.872664. . .). In this article, we will discuss the methods to find the value of cot 50 degrees with examples.

Cot 50° in decimal: 0.8390996. . .
Cot (-50 degrees): -0.8390996. . .
Cot 50° in radians: cot (5π/18) or cot (0.8726646 . . .)

What is the Value of Cot 50 Degrees?

The value of cot 50 degrees in decimal is 0.839099631. . .. Cot 50 degrees can also be expressed using the equivalent of the given angle (50 degrees) in radians (0.87266 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 50 degrees = 50° × (π/180°) rad = 5π/18 or 0.8726 . . .
∴ cot 50° = cot(0.8726) = 0.8390996. . .

Explanation:

For cot 50 degrees, the angle 50° lies between 0° and 90° (First Quadrant). Since cotangent function is positive in the first quadrant, thus cot 50° value = 0.8390996. . .
Since the cotangent function is a periodic function, we can represent cot 50° as, cot 50 degrees = cot(50° + n × 180°), n ∈ Z.
⇒ cot 50° = cot 230° = cot 410°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-50°) = -cot(50°).

Methods to Find Value of Cot 50 Degrees

The cotangent function is positive in the 1st quadrant. The value of cot 50° is given as 0.83909. . . We can find the value of cot 50 degrees by:

Using Unit Circle
Using Trigonometric Functions

Cot 50 Degrees Using Unit Circle

To find the value of cot 50 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 50° angle with the positive x-axis.
The cot of 50 degrees equals the x-coordinate(0.6428) divided by y-coordinate(0.766) of the point of intersection (0.6428, 0.766) of unit circle and r.

Hence the value of cot 50° = x/y = 0.8391 (approx).

Cot 50° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 50 degrees as:

cos(50°)/sin(50°)
± cos 50°/√(1 - cos²(50°))
± √(1 - sin²(50°))/sin 50°
± 1/√(sec²(50°) - 1)
± √(cosec²(50°) - 1)
1/tan 50°

Note: Since 50° lies in the 1st Quadrant, the final value of cot 50° will be positive.

We can use trigonometric identities to represent cot 50° as,

tan (90° - 50°) = tan 40°
-tan (90° + 50°) = -tan 140°
-cot (180° - 50°) = -cot 130°

☛ Also Check:

Examples Using Cot 50 Degrees

Example 1: Find the value of (cos (50°) cosec (25°) sec (25°))/2. [Hint: Use cot 50° = 0.8391]

Solution:

Using trigonometry formulas,
(cos (50°) cosec (25°) sec (25°))/2 = cos (50°)/(2 sin (25°) cos (25°))
Using sin 2a formula,
2 sin (25°) cos (25°) = sin (2 × 25°) = sin 50°
⇒ cos (50°) / sin (50°) = cot 50°
⇒ (cos (50°) cosec (25°) sec (25°))/2 = 0.8391
Example 2: Using the value of cot 50°, solve: (cosec²(50°) - 1).

Solution:
We know, (cosec²(50°) - 1) = (cot²(50°)) = 0.7041
⇒ (cosec²(50°) - 1) = 0.7041
Example 3: Simplify: 5 (cot 50°/tan 40°)

Solution:

We know cot 50° = tan 40°
⇒ 5 cot 50°/tan 40° = 5 (cot 50°/cot 50°)
= 5(1) = 5

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FAQs on Cot 50 Degrees

What is Cot 50 Degrees?

Cot 50 degrees is the value of cotangent trigonometric function for an angle equal to 50 degrees. The value of cot 50° is 0.8391 (approx).

What is the Value of Cot 50° in Terms of Sec 50°?

We can represent the cotangent function in terms of the secant function using trig identities, cot 50° can be written as 1/√(sec²(50°) - 1). Here, the value of sec 50° is equal to 1.5557.

How to Find the Value of Cot 50 Degrees?

The value of cot 50 degrees can be calculated by constructing an angle of 50° with the x-axis, and then finding the coordinates of the corresponding point (0.6428, 0.766) on the unit circle. The value of cot 50° is equal to the x-coordinate(0.6428) divided by the y-coordinate (0.766). ∴ cot 50° = 0.8391

What is the Value of Cot 50 Degrees in Terms of Sin 50°?

Using trigonometric identities, we can write cot 50° in terms of sin 50° as, cot(50°) = √(1 - sin²(50°))/sin 50° . Here, the value of sin 50° is equal to 0.766.

How to Find Cot 50° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 50° can be given in terms of other trigonometric functions as:

cos(50°)/sin(50°)
± cos 50°/√(1 - cos²(50°))
± √(1 - sin²(50°))/sin 50°
± 1/√(sec²(50°) - 1)
± √(cosec²(50°) - 1)
1/tan 50°

☛ Also check: trigonometry table

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