The value of cosec pi/6 is 2. Cosec pi/6 radians in degrees is written as cosec ((π/6) × 180°/π), i.e., cosec (30°). In this article, we will discuss the methods lớn find the value of csc pi/6 with examples.
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What is the Value of Cosec pi/6?
The value of csc pi/6 is 2. Cosec pi/6 can also be expressed using the equivalent of the given angle (pi/6) in degrees (30°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)⇒ pi/6 radians = pi/6 × (180°/pi) = 30° or 30 degrees∴ csc pi/6 = csc π/6 = csc(30°) = 2
Explanation:
For csc pi/6, the angle pi/6 lies between 0 và pi/2 (First Quadrant). Since cosecant function is positive in the first quadrant, thus cosec pi/6 value = 2Since the cosecant function is a periodic function, we can represent csc pi/6 as, cosec pi/6 = csc(pi/6 + n × 2pi), n ∈ Z.⇒ csc pi/6 = csc 13pi/6 = cosec 25pi/6 , & so on.Note: Since, cosecant is an odd function, the value of cosec(-pi/6) = -cosec(pi/6).
Methods lớn Find Value of Cosec pi/6
The cosecant function is positive in the 1st quadrant. The value of cosec pi/6 is given as 2. We can find the value of csc pi/6 by:
Using Unit CircleUsing Trigonometric FunctionsCosec pi/6 Using Unit Circle
To find the value of cosec π/6 using the unit circle:
Rotate ‘r’ anticlockwise to form pi/6 angle with the positive x-axis.The cosec of pi/6 equals the reciprocal of the y-coordinate(0.5) of the point of intersection (0.866, 0.5) of unit circle và r.Hence the value of cosec pi/6 = 1/y = 2
Cosec pi/6 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cosec pi/6 as:
± 1/√(1-cos²(pi/6))± √(1 + tan²(pi/6))/tan(pi/6)± √(1 + cot²(pi/6))± sec(pi/6)/√(sec²(pi/6) - 1))1/sin(pi/6)Note: Since pi/6 lies in the 1st Quadrant, the final value of csc pi/6 will be positive.
We can use trigonometric identities lớn represent csc pi/6 as,
csc(pi - pi/6) = cosec 5pi/6-cosec(pi + pi/6) = -cosec 7pi/6sec(pi/2 - pi/6) = sec pi/3-sec(pi/2 + pi/6) = -sec 2pi/3☛ Also Check:
FAQs on Cosec pi/6
What is Cosec pi/6?
Cosec pi/6 is the value of cosecant trigonometric function for an angle equal lớn π/6. The value of cosec pi/6 is 2.
How to lớn Find Cosec pi/6 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of csc pi/6 can be given in terms of other trigonometric functions as:
± 1/√(1-cos²(pi/6))± √(1 + tan²(pi/6))/tan(pi/6)± √(1 + cot²(pi/6))± sec(pi/6)/√(sec²(pi/6) - 1))1/sin(pi/6)☛ Also check: trigonometry table
What is the Value of Cosec pi/6 in Terms of Sec pi/6?
Since the csc function can be represented using the secant function, we can write csc pi/6 as sec(pi/6)/√(sec²(pi/6) - 1). The value of sec pi/6 is equal to 1.1547.
What is the Value of Csc pi/6 in Terms of Cos pi/6?
Using trigonometric identities, we can write csc pi/6 in terms of cos pi/6 as, csc(pi/6) = 1/√(1 - cos²(pi/6)). Here, the value of cos pi/6 is equal lớn 0.866.
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How lớn Find the Value of Cosec pi/6?
The value of csc pi/6 can be calculated by constructing an angle of π/6 radians with the x-axis, & then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of csc pi/6 is equal khổng lồ the reciprocal of the y-coordinate (0.5). ∴ csc pi/6 = 2.