11 Pi 2 In Degrees

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.eastward., sin (990°). In this commodity, we will discuss the methods to observe the value of sin 11pi/2 with examples.

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

What is the Value of Sin 11pi/ii?

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

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

Sin 11pi/2

Explanation:

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

Methods to Detect Value of Sin 11pi/2

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

Using Trigonometric Functions
Using Unit Circle

Sin 11pi/two in Terms of Trigonometric Functions

Using trigonometry formulas, nosotros can represent the sin 11pi/2 every bit:

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

Notation: Since 11pi/ii lies on the negative y-axis, the final value of sin 11pi/ii is -ane.

Nosotros tin can utilize trigonometric identities to represent sin 11pi/2 as,

sin(pi - 11pi/two) = sin(-9pi/two)
-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

value of sin 11pi/2

To notice the value of sin 11π/2 using the unit circle, represent 11pi/2 in the course (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 bending with the positive x-axis.
The sin of 11pi/ii equals the y-coordinate(-ane) of the signal of intersection (0, -1) of unit circle and r.

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

☛ Also Bank check:

tan 7pi/half-dozen
sin pi/12
cos 11pi/4
sin 2pi
cos pi/iv
cos 2pi/3

FAQs on Sin 11pi/ii

What is Sin 11pi/two?

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

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

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

± √(i-cos²(11pi/2))
± tan(11pi/ii)/√(1 + tan²(11pi/two))
± one/√(i + cot²(11pi/2))
± √(sec²(11pi/ii) - ane)/sec(11pi/2)
1/cosec(11pi/2)

☛ Also bank check: trigonometry table

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

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

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

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