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Cot 132 Degrees

The value of cot 132 degrees is -0.9004040. . .. Cot 132 degrees in radians is written as cot (132° × π/180°), i.e., cot (11π/15) or cot (2.303834. . .). In this article, we will discuss the methods to find the value of cot 132 degrees with examples.

Cot 132° in decimal: -0.9004040. . .
Cot (-132 degrees): 0.9004040. . .
Cot 132° in radians: cot (11π/15) or cot (2.3038346 . . .)

What is the Value of Cot 132 Degrees?

The value of cot 132 degrees in decimal is -0.900404044. . .. Cot 132 degrees can also be expressed using the equivalent of the given angle (132 degrees) in radians (2.30383 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 132 degrees = 132° × (π/180°) rad = 11π/15 or 2.3038 . . .
∴ cot 132° = cot(2.3038) = -0.9004040. . .

Explanation:

For cot 132 degrees, the angle 132° lies between 90° and 180° (Second Quadrant). Since cotangent function is negative in the second quadrant, thus cot 132° value = -0.9004040. . .
Since the cotangent function is a periodic function, we can represent cot 132° as, cot 132 degrees = cot(132° + n × 180°), n ∈ Z.
⇒ cot 132° = cot 312° = cot 492°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-132°) = -cot(132°).

Methods to Find Value of Cot 132 Degrees

The cotangent function is negative in the 2nd quadrant. The value of cot 132° is given as -0.90040. . . We can find the value of cot 132 degrees by:

Using Unit Circle
Using Trigonometric Functions

Cot 132 Degrees Using Unit Circle

To find the value of cot 132 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 132° angle with the positive x-axis.
The cot of 132 degrees equals the x-coordinate(-0.6691) divided by y-coordinate(0.7431) of the point of intersection (-0.6691, 0.7431) of unit circle and r.

Hence the value of cot 132° = x/y = -0.9004 (approx).

Cot 132° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cot 132 degrees as:

cos(132°)/sin(132°)
± cos 132°/√(1 - cos²(132°))
± √(1 - sin²(132°))/sin 132°
± 1/√(sec²(132°) - 1)
± √(cosec²(132°) - 1)
1/tan 132°

Note: Since 132° lies in the 2nd Quadrant, the final value of cot 132° will be negative.

We can use trigonometric identities to represent cot 132° as,

tan (90° - 132°) = tan(-42°)
-tan (90° + 132°) = -tan 222°
-cot (180° - 132°) = -cot 48°

☛ Also Check:

Examples Using Cot 132 Degrees

Example 1: Using the value of cot 132°, solve: (cosec²(132°) - 1).

Solution:
We know, (cosec²(132°) - 1) = (cot²(132°)) = 0.8107
⇒ (cosec²(132°) - 1) = 0.8107
Example 2: Find the value of (cos (132°) cosec (66°) sec (66°))/2. [Hint: Use cot 132° = -0.9004]

Solution:

Using trigonometry formulas,
(cos (132°) cosec (66°) sec (66°))/2 = cos (132°)/(2 sin (66°) cos (66°))
Using sin 2a formula,
2 sin (66°) cos (66°) = sin (2 × 66°) = sin 132°
⇒ cos (132°) / sin (132°) = cot 132°
⇒ (cos (132°) cosec (66°) sec (66°))/2 = -0.9004
Example 3: Find the value of cot 132° if tan 132° is -1.1106.

Solution:
Since, cot 132° = 1/tan 132°
⇒ cot 132° = 1/(-1.1106) = -0.9004

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FAQs on Cot 132 Degrees

What is Cot 132 Degrees?

Cot 132 degrees is the value of cotangent trigonometric function for an angle equal to 132 degrees. The value of cot 132° is -0.9004 (approx).

What is the Exact Value of Cot 132 Degrees?

The exact value of cot 132 degrees can be given accurately up to 8 decimal places as -0.90040404.

How to Find Cot 132° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cot 132° can be given in terms of other trigonometric functions as:

cos(132°)/sin(132°)
± cos 132°/√(1 - cos²(132°))
± √(1 - sin²(132°))/sin 132°
± 1/√(sec²(132°) - 1)
± √(cosec²(132°) - 1)
1/tan 132°

☛ Also check: trigonometry table

What is the Value of Cot 132 Degrees in Terms of Cos 132°?

We know, using trig identities, we can write cot 132° as cos 132°/√(1 - cos²(132°)). Here, the value of cos 132° is equal to -0.669130.

How to Find the Value of Cot 132 Degrees?

The value of cot 132 degrees can be calculated by constructing an angle of 132° with the x-axis, and then finding the coordinates of the corresponding point (-0.6691, 0.7431) on the unit circle. The value of cot 132° is equal to the x-coordinate(-0.6691) divided by the y-coordinate (0.7431). ∴ cot 132° = -0.9004

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