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Sin 7pi/2
The value of sin 7pi/2 is 1. Sin 7pi/2 radians in degrees is written as sin ((7π/2) × 180°/π), i.e., sin (630°). In this article, we will discuss the methods to find the value of sin 7pi/2 with examples.
 Sin 7pi/2: 1
 Sin (7pi/2): 1
 Sin 7pi/2 in degrees: sin (630°)
What is the Value of Sin 7pi/2?
The value of sin 7pi/2 is 1. Sin 7pi/2 can also be expressed using the equivalent of the given angle (7pi/2) in degrees (630°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi/2 radians = 7pi/2 × (180°/pi) = 630° or 630 degrees
∴ sin 7pi/2 = sin 7π/2 = sin(630°) = 1
Explanation:
For sin 7pi/2, the angle 7pi/2 > 2pi. We can represent sin 7pi/2 as, sin(7pi/2 mod 2pi) = sin(3pi/2). For sin 7pi/2, the angle 7pi/2 lies on the negative yaxis. Thus, sin 7pi/2 value = 1
Since the sine function is a periodic function, we can represent sin 7pi/2 as, sin 7pi/2 = sin(7pi/2 + n × 2pi), n ∈ Z.
⇒ sin 7pi/2 = sin 11pi/2 = sin 15pi/2 , and so on.
Note: Since, sine is an odd function, the value of sin(7pi/2) = sin(7pi/2).
Methods to Find Value of Sin 7pi/2
The value of sin 7pi/2 is given as 1. We can find the value of sin 7pi/2 by:
 Using Unit Circle
 Using Trigonometric Functions
Sin 7pi/2 Using Unit Circle
To find the value of sin 7π/2 using the unit circle, represent 7pi/2 in the form (1 × 2pi) + 3pi/2 [∵ 7pi/2>2pi] ∵ sine is a periodic function, sin 7pi/2 = sin 3pi/2.
 Rotate ‘r’ anticlockwise to form 3pi/2 or 7pi/2 angle with the positive xaxis.
 The sin of 7pi/2 equals the ycoordinate(1) of the point of intersection (0, 1) of unit circle and r.
Hence the value of sin 7pi/2 = y = 1
Sin 7pi/2 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 7pi/2 as:
 ± √(1cos²(7pi/2))
 ± tan(7pi/2)/√(1 + tan²(7pi/2))
 ± 1/√(1 + cot²(7pi/2))
 ± √(sec²(7pi/2)  1)/sec(7pi/2)
 1/cosec(7pi/2)
Note: Since 7pi/2 lies on the negative yaxis, the final value of sin 7pi/2 is 1.
We can use trigonometric identities to represent sin 7pi/2 as,
 sin(pi  7pi/2) = sin(5pi/2)
 sin(pi + 7pi/2) = sin 9pi/2
 cos(pi/2  7pi/2) = cos(3pi)
 cos(pi/2 + 7pi/2) = cos 4pi
☛ Also Check:
Examples Using Sin 7pi/2

Example 1: Find the value of 5 sin(7pi/2)/7 cos(3pi).
Solution:
Using trigonometric identities, we know, sin(7pi/2) = cos(pi/2  7pi/2) = cos(3pi).
⇒ sin(7pi/2) = cos(3pi)
⇒ Value of 5 sin(7pi/2)/7 cos(3pi) = 5/7 
Example 2: Using the value of sin 7pi/2, solve: (1cos²(7pi/2)).
Solution:
We know, (1cos²(7pi/2)) = (sin²(7pi/2)) = 1
⇒ (1cos²(7pi/2)) = 1 
Example 3: Find the value of sin(7pi/2) if cosec(7pi/2) is 1.
Solution:
Since, sin 7pi/2 = 1/csc(7pi/2)
⇒ sin 7pi/2 = 1/(1) = 1
FAQs on Sin 7pi/2
What is Sin 7pi/2?
Sin 7pi/2 is the value of sine trigonometric function for an angle equal to 7pi/2 radians. The value of sin 7pi/2 is 1.
What is the Value of Sin 7pi/2 in Terms of Sec 7pi/2?
Since the sine function can be represented using the secant function, we can write sin 7pi/2 as √(sec²(7pi/2)  1)/sec 7pi/2.
How to Find the Value of Sin 7pi/2?
The value of sin 7pi/2 can be calculated by constructing an angle of 7π/2 radians with the xaxis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sin 7pi/2 is equal to the ycoordinate (1). ∴ sin 7pi/2 = 1.
What is the Value of Sin 7pi/2 in Terms of Cot 7pi/2?
We can represent the sine function in terms of the cotangent function using trig identities, sin 7pi/2 can be written as 1/√(1 + cot²(7pi/2)). Here, the value of cot 7pi/2 is equal to 0.
How to Find Sin 7pi/2 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 7π/2 can be given in terms of other trigonometric functions as:
 ± √(1cos²(7pi/2))
 ± tan(7pi/2)/√(1 + tan²(7pi/2))
 ± 1/√(1 + cot²(7pi/2))
 ± √(sec²(7pi/2)  1)/sec(7pi/2)
 1/cosec(7pi/2)
☛ Also check: trigonometry table
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