Sin 9pi/2
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°) = 1Explanation: 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:
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.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: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,☛ Also Check:
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