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Sec 75 Degrees
The value of Sec 75 degrees is 3.8637033. . .. Sec 75 degrees in radians is written as sec (75° × π/180°), i.e., sec (5π/12) or sec (1.308996. . .). In this article, we will discuss the methods to find the value of sec 75 degrees with examples.
 Sec 75°: √6 + √2
 Sec 75° in decimal: 3.8637033. . .
 Sec (75 degrees): 3.8637033. . . or √6 + √2
 Sec 75° in radians: sec (5π/12) or sec (1.3089969 . . .)
What is the Value of Sec 75 Degrees?
The value of sec 75 degrees in decimal is 3.863703305. . .. Sec 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 . . .
∴ sec 75° = sec(1.3089) = √6 + √2 or 3.8637033. . .
Explanation:
For sec 75 degrees, the angle 75° lies between 0° and 90° (First Quadrant). Since secant function is positive in the first quadrant, thus sec 75° value = √6 + √2 or 3.8637033. . .
Since the secant function is a periodic function, we can represent sec 75° as, sec 75 degrees = sec(75° + n × 360°), n ∈ Z.
⇒ sec 75° = sec 435° = sec 795°, and so on.
Note: Since, secant is an even function, the value of sec(75°) = sec(75°).
Methods to Find Value of Sec 75 Degrees
The secant function is positive in the 1st quadrant. The value of sec 75° is given as 3.86370. . .. We can find the value of sec 75 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Sec 75 Degrees Using Unit Circle
To find the value of sec 75 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 75° angle with the positive xaxis.
 The sec of 75 degrees equals the reciprocal of the xcoordinate(0.2588) of the point of intersection (0.2588, 0.9659) of unit circle and r.
Hence the value of sec 75° = 1/x = 3.8637 (approx)
Sec 75° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sec 75 degrees as:
 ± 1/√(1  sin²(75°))
 ± √(1 + tan²(75°))
 ± √(1 + cot²(75°))/cot 75°
 ± cosec 75°/√(cosec²(75°)  1)
 1/cos 75°
Note: Since 75° lies in the 1st Quadrant, the final value of sec 75° will be positive.
We can use trigonometric identities to represent sec 75° as,
 sec(180°  75°) = sec 105°
 sec(180° + 75°) = sec 255°
 cosec(90° + 75°) = cosec 165°
 cosec(90°  75°) = cosec 15°
☛ Also Check:
Examples Using Sec 75 Degrees

Example 1: Find the value of sec 75° if cos 75° is 0.2588.
Solution:
Since, sec 75° = 1/cos 75°
⇒ sec 75° = 1/0.2588 = 3.8637 
Example 2: Using the value of sec 75°, solve: (1 + tan²(75°)).
Solution:
We know, (1 + tan²(75°)) = (sec²(75°)) = 14.9282
⇒ (1 + tan²(75°)) = 14.9282 
Example 3: Simplify: 8 (sec 75°/cosec 165°)
Solution:
We know sec 75° = cosec 165°
⇒ 8 sec 75°/cosec 165° = 8 (sec 75°/sec 75°)
= 8(1) = 8
FAQs on Sec 75 Degrees
What is Sec 75 Degrees?
Sec 75 degrees is the value of secant trigonometric function for an angle equal to 75 degrees. The value of sec 75° is √6 + √2 or 3.8637 (approx).
What is the Exact Value of Sec 75 Degrees?
The exact value of sec 75 degrees can be given accurately up to 8 decimal places as 3.86370330 or as √6 + √2.
How to Find the Value of Sec 75 Degrees?
The value of sec 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 sec 75° is equal to the reciprocal of the xcoordinate(0.2588). ∴ sec 75° = 3.8637.
What is the Value of Sec 75 Degrees in Terms of Sin 75°?
Using trigonometric identities, we can write sec 75° in terms of sin 75° as, sec(75°) = 1/√(1  sin²(75°)). Here, the value of sin 75° is equal to 0.9659.
How to Find Sec 75° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sec 75° can be given in terms of other trigonometric functions as:
 ± 1/√(1sin²(75°))
 ± √(1 + tan²(75°))
 ± √(1 + cot²(75°))/cot 75°
 ± cosec 75°/√(cosec²(75°)  1)
 1/cos 75°
☛ Also check: trigonometric table
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