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Cosec 75 Degrees
The value of cosec 75 degrees is 1.0352761. . .. Cosec 75 degrees in radians is written as cosec (75° × π/180°), i.e., cosec (5π/12) or cosec (1.308996. . .). In this article, we will discuss the methods to find the value of cosec 75 degrees with examples.
 Cosec 75°: √6  √2
 Cosec 75° in decimal: 1.0352761. . .
 Cosec (75 degrees): 1.0352761. . . or (√6  √2)
 Cosec 75° in radians: cosec (5π/12) or cosec (1.3089969 . . .)
What is the Value of Cosec 75 Degrees?
The value of cosec 75 degrees in decimal is 1.035276180. . .. Cosec 75 degrees can also be expressed using the equivalent of the given angle (75 degrees) in radians (1.30899 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 75 degrees = 75° × (π/180°) rad = 5π/12 or 1.3089 . . .
∴ cosec 75° = cosec(1.3089) = √6  √2 or 1.0352761. . .
Explanation:
For cosec 75 degrees, the angle 75° lies between 0° and 90° (First Quadrant). Since cosecant function is positive in the first quadrant, thus cosec 75° value = √6  √2 or 1.0352761. . .
Since the cosecant function is a periodic function, we can represent cosec 75° as, cosec 75 degrees = cosec(75° + n × 360°), n ∈ Z.
⇒ cosec 75° = cosec 435° = cosec 795°, and so on.
Note: Since, cosecant is an odd function, the value of cosec(75°) = cosec(75°).
Methods to Find Value of Cosec 75 Degrees
The cosecant function is positive in the 1st quadrant. The value of cosec 75° is given as 1.03527. . .. We can find the value of cosec 75 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Cosec 75 Degrees Using Unit Circle
To find the value of cosec 75 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 75° angle with the positive xaxis.
 The cosec of 75 degrees equals the reciprocal of the ycoordinate(0.9659) of the point of intersection (0.2588, 0.9659) of unit circle and r.
Hence the value of cosec 75° = 1/y = 1.0353 (approx)
Cosec 75° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cosec 75 degrees as:
 ± 1/√(1cos²(75°))
 ± √(1 + tan²(75°))/tan 75°
 ± √(1 + cot²(75°))
 ± sec 75°/√(sec²(75°)  1)
 1/sin 75°
Note: Since 75° lies in the 1st Quadrant, the final value of cosec 75° will be positive.
We can use trigonometric identities to represent cosec 75° as,
 cosec(180°  75°) = cosec 105°
 cosec(180° + 75°) = cosec 255°
 sec(90°  75°) = sec 15°
 sec(90° + 75°) = sec 165°
☛ Also Check:
Examples Using Cosec 75 Degrees

Example 1: Using the value of csc 75°, solve: (1 + cot²(75°)).
Solution:
We know, (1 + cot²(75°)) = (csc²(75°)) = 1.0718
⇒ (1 + cot²(75°)) = 1.0718 
Example 2: Find the value of csc 75° if sin 75° is 0.9659.
Solution:
Since, csc 75° = 1/sin 75°
⇒ csc 75° = 1/0.9659 = 1.0353 
Example 3: Find the value of (sec 37.5° cosec 37.5°)/2. [Hint: Use cosec 75° = 1.0353]
Solution:
Using the sin 2a formula,
(sec 37.5° cosec 37.5°)/2 = 1/(2 × cos 37.5° sin 37.5°) = 1/sin 75°
= 1/sin 75° = cosec 75° = 1.0353
⇒ (sec 37.5° cosec 37.5°)/2 = 1.0353
FAQs on Cosec 75 Degrees
What is Cosec 75 Degrees?
Cosec 75 degrees is the value of cosecant trigonometric function for an angle equal to 75 degrees. The value of cosec 75° is √6  √2 or 1.0353 (approx).
What is the Value of Cosec 75 Degrees in Terms of Tan 75°?
We know, using trig identities, we can write cosec 75° as √(1 + tan²(75°))/tan 75°. Here, the value of tan 75° is equal to 3.7321.
What is the Value of Csc 75° in Terms of Sin 75°?
Since the cosecant function is the reciprocal of the sine function, we can write csc 75° as 1/sin(75°). The value of sin 75° is equal to 0.9659.
How to Find Cosec 75° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cosec 75° can be given in terms of other trigonometric functions as:
 ± 1/√(1cos²(75°))
 ± √(1 + tan²(75°))/tan 75°
 ± √(1 + cot²(75°))
 ± sec 75°/√(sec²(75°)  1)
 1/sin 75°
☛ Also check: trigonometry table
How to Find the Value of Cosec 75 Degrees?
The value of cosec 75 degrees can be calculated by constructing an angle of 75° with the xaxis, and then finding the coordinates of the corresponding point (0.2588, 0.9659) on the unit circle. The value of cosec 75° is equal to the reciprocal of the ycoordinate (0.9659). ∴ cosec 75° = 1.0353.
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