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
