Sin 11pi/2

The value of sin 11pi/2 is -1. Sin 11pi/2 radians in degrees is written as sin ((11π/2) × 180°/π), i.e., sin (990°). In this article, we will discuss the methods to find the value of sin 11pi/2 with examples.

• Sin 11pi/2: -1
• Sin (-11pi/2): 1
• Sin 11pi/2 in degrees: sin (990°)

What is the Value of Sin 11pi/2?

The value of sin 11pi/2 is -1. Sin 11pi/2 can also be expressed using the equivalent of the given angle (11pi/2) in degrees (990°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 11pi/2 radians = 11pi/2 × (180°/pi) = 990° or 990 degrees
∴ sin 11pi/2 = sin 11π/2 = sin(990°) = -1

Explanation:

For sin 11pi/2, the angle 11pi/2 > 2pi. We can represent sin 11pi/2 as, sin(11pi/2 mod 2pi) = sin(3pi/2). For sin 11pi/2, the angle 11pi/2 lies on the negative y-axis. Thus, sin 11pi/2 value = -1
Since the sine function is a periodic function, we can represent sin 11pi/2 as, sin 11pi/2 = sin(11pi/2 + n × 2pi), n ∈ Z.
⇒ sin 11pi/2 = sin 15pi/2 = sin 19pi/2 , and so on.
Note: Since, sine is an odd function, the value of sin(-11pi/2) = -sin(11pi/2).

Methods to Find Value of Sin 11pi/2

The value of sin 11pi/2 is given as -1. We can find the value of sin 11pi/2 by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 11pi/2 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 11pi/2 as:

• ± √(1-cos²(11pi/2))
• ± tan(11pi/2)/√(1 + tan²(11pi/2))
• ± 1/√(1 + cot²(11pi/2))
• ± √(sec²(11pi/2) - 1)/sec(11pi/2)
• 1/cosec(11pi/2)

Note: Since 11pi/2 lies on the negative y-axis, the final value of sin 11pi/2 is -1.

We can use trigonometric identities to represent sin 11pi/2 as,

• sin(pi - 11pi/2) = sin(-9pi/2)
• -sin(pi + 11pi/2) = -sin 13pi/2
• cos(pi/2 - 11pi/2) = cos(-5pi)
• -cos(pi/2 + 11pi/2) = -cos 6pi

Sin 11pi/2 Using Unit Circle

To find the value of sin 11π/2 using the unit circle, represent 11pi/2 in the form (2 × 2pi) + 3pi/2 [∵ 11pi/2>2pi] ∵ sine is a periodic function, sin 11pi/2 = sin 3pi/2.

• Rotate ‘r’ anticlockwise to form 3pi/2 or 11pi/2 angle with the positive x-axis.
• The sin of 11pi/2 equals the y-coordinate(-1) of the point of intersection (0, -1) of unit circle and r.

Hence the value of sin 11pi/2 = y = -1

☛ Also Check:

• tan 7pi/6
• sin pi/12
• cos 11pi/4
• sin 2pi
• cos pi/4
• cos 2pi/3

FAQs on Sin 11pi/2

What is Sin 11pi/2?

Sin 11pi/2 is the value of sine trigonometric function for an angle equal to 11pi/2 radians. The value of sin 11pi/2 is -1.

How to Find the Value of Sin 11pi/2?

The value of sin 11pi/2 can be calculated by constructing an angle of 11π/2 radians with the x-axis, and then finding the coordinates of the corresponding point (0, -1) on the unit circle. The value of sin 11pi/2 is equal to the y-coordinate (-1). ∴ sin 11pi/2 = -1.

How to Find Sin 11pi/2 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 11π/2 can be given in terms of other trigonometric functions as:

• ± √(1-cos²(11pi/2))
• ± tan(11pi/2)/√(1 + tan²(11pi/2))
• ± 1/√(1 + cot²(11pi/2))
• ± √(sec²(11pi/2) - 1)/sec(11pi/2)
• 1/cosec(11pi/2)

☛ Also check: trigonometry table

What is the Value of Sin 11pi/2 in Terms of Cosec 11pi/2?

Since the cosecant function is the reciprocal of the sine function, we can write sin 11pi/2 as 1/cosec(11pi/2). The value of cosec 11pi/2 is equal to -1.

What is the Value of Sin 11pi/2 in Terms of Cos 11pi/2?

Using trigonometric identities, we can write sin 11pi/2 in terms of cos 11pi/2 as, sin(11pi/2) = -√(1-cos²(11pi/2)). Here, the value of cos 11pi/2 is equal to 0.