Sin 9pi/2

The value of sin 9pi/2 is 1. Sin 9pi/2 radians in degrees is written as sin ((9π/2) × 180°/π), i.e., sin (810°). In this article, we will discuss the methods to find the value of sin 9pi/2 with examples.

• Sin 9pi/2: 1
• Sin (-9pi/2): -1
• Sin 9pi/2 in degrees: sin (810°)

What is the Value of Sin 9pi/2?

The value of sin 9pi/2 is 1. Sin 9pi/2 can also be expressed using the equivalent of the given angle (9pi/2) in degrees (810°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 9pi/2 radians = 9pi/2 × (180°/pi) = 810° or 810 degrees
∴ sin 9pi/2 = sin 9π/2 = sin(810°) = 1

Explanation:

For sin 9pi/2, the angle 9pi/2 > 2pi. We can represent sin 9pi/2 as, sin(9pi/2 mod 2pi) = sin(pi/2). For sin 9pi/2, the angle 9pi/2 lies on the positive y-axis. Thus, sin 9pi/2 value = 1
Since the sine function is a periodic function, we can represent sin 9pi/2 as, sin 9pi/2 = sin(9pi/2 + n × 2pi), n ∈ Z.
⇒ sin 9pi/2 = sin 13pi/2 = sin 17pi/2 , and so on.
Note: Since, sine is an odd function, the value of sin(-9pi/2) = -sin(9pi/2).

Methods to Find Value of Sin 9pi/2

The value of sin 9pi/2 is given as 1. We can find the value of sin 9pi/2 by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 9pi/2 Using Unit Circle

To find the value of sin 9π/2 using the unit circle, represent 9pi/2 in the form (2 × 2pi) + pi/2 [∵ 9pi/2>2pi] ∵ sine is a periodic function, sin 9pi/2 = sin pi/2.

• Rotate ‘r’ anticlockwise to form pi/2 or 9pi/2 angle with the positive x-axis.
• The sin of 9pi/2 equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.

Hence the value of sin 9pi/2 = y = 1

Sin 9pi/2 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 9pi/2 as:

• ± √(1-cos²(9pi/2))
• ± tan(9pi/2)/√(1 + tan²(9pi/2))
• ± 1/√(1 + cot²(9pi/2))
• ± √(sec²(9pi/2) - 1)/sec(9pi/2)
• 1/cosec(9pi/2)

Note: Since 9pi/2 lies on the positive y-axis, the final value of sin 9pi/2 is 1.

We can use trigonometric identities to represent sin 9pi/2 as,

• sin(pi - 9pi/2) = sin(-7pi/2)
• -sin(pi + 9pi/2) = -sin 11pi/2
• cos(pi/2 - 9pi/2) = cos(-4pi)
• -cos(pi/2 + 9pi/2) = -cos 5pi

☛ Also Check:

• sin 9pi/2
• sin 5pi/8
• sin 11pi/2
• cot 5pi/4
• sin pi/3
• csc pi/2

FAQs on Sin 9pi/2

What is Sin 9pi/2?

Sin 9pi/2 is the value of sine trigonometric function for an angle equal to 9pi/2 radians. The value of sin 9pi/2 is 1.

What is the Value of Sin 9pi/2 in Terms of Cos 9pi/2?

Using trigonometric identities, we can write sin 9pi/2 in terms of cos 9pi/2 as, sin(9pi/2) = √(1-cos²(9pi/2)). Here, the value of cos 9pi/2 is equal to 0.

How to Find the Value of Sin 9pi/2?

The value of sin 9pi/2 can be calculated by constructing an angle of 9π/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 9pi/2 is equal to the y-coordinate (1). ∴ sin 9pi/2 = 1.

How to Find Sin 9pi/2 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 9π/2 can be given in terms of other trigonometric functions as:

• ± √(1-cos²(9pi/2))
• ± tan(9pi/2)/√(1 + tan²(9pi/2))
• ± 1/√(1 + cot²(9pi/2))
• ± √(sec²(9pi/2) - 1)/sec(9pi/2)
• 1/cosec(9pi/2)

☛ Also check: trigonometric table

What is the Value of Sin 9pi/2 in Terms of Sec 9pi/2?

Since the sine function can be represented using the secant function, we can write sin 9pi/2 as √(sec²(9pi/2) - 1)/sec 9pi/2.