Sin 7pi/4
The value of sin 7pi/4 is 0.7071067. . .. Sin 7pi/4 radians in degrees is written as sin ((7π/4) × 180°/π), i.e., sin (315°). In this article, we will discuss the methods to find the value of sin 7pi/4 with examples.
 Sin 7pi/4: (1/√2)
 Sin 7pi/4 in decimal: 0.7071067. . .
 Sin (7pi/4): 0.7071067. . . or 1/√2
 Sin 7pi/4 in degrees: sin (315°)
What is the Value of Sin 7pi/4?
The value of sin 7pi/4 in decimal is 0.707106781. . .. Sin 7pi/4 can also be expressed using the equivalent of the given angle (7pi/4) in degrees (315°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi/4 radians = 7pi/4 × (180°/pi) = 315° or 315 degrees
∴ sin 7pi/4 = sin 7π/4 = sin(315°) = (1/√2) or 0.7071067. . .
Explanation:
For sin 7pi/4, the angle 7pi/4 lies between 3pi/2 and 2pi (Fourth Quadrant). Since sine function is negative in the fourth quadrant, thus sin 7pi/4 value = (1/√2) or 0.7071067. . .
Since the sine function is a periodic function, we can represent sin 7pi/4 as, sin 7pi/4 = sin(7pi/4 + n × 2pi), n ∈ Z.
⇒ sin 7pi/4 = sin 15pi/4 = sin 23pi/4 , and so on.
Note: Since, sine is an odd function, the value of sin(7pi/4) = sin(7pi/4).
Methods to Find Value of Sin 7pi/4
The sine function is negative in the 4th quadrant. The value of sin 7pi/4 is given as 0.70710. . .. We can find the value of sin 7pi/4 by:
 Using Trigonometric Functions
 Using Unit Circle
Sin 7pi/4 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 7pi/4 as:
 ± √(1cos²(7pi/4))
 ± tan(7pi/4)/√(1 + tan²(7pi/4))
 ± 1/√(1 + cot²(7pi/4))
 ± √(sec²(7pi/4)  1)/sec(7pi/4)
 1/cosec(7pi/4)
Note: Since 7pi/4 lies in the 4th Quadrant, the final value of sin 7pi/4 will be negative.
We can use trigonometric identities to represent sin 7pi/4 as,
 sin(pi  7pi/4) = sin(3pi/4)
 sin(pi + 7pi/4) = sin 11pi/4
 cos(pi/2  7pi/4) = cos(5pi/4)
 cos(pi/2 + 7pi/4) = cos 9pi/4
Sin 7pi/4 Using Unit Circle
To find the value of sin 7π/4 using the unit circle:
 Rotate ‘r’ anticlockwise to form 7pi/4 angle with the positive xaxis.
 The sin of 7pi/4 equals the ycoordinate(0.7071) of the point of intersection (0.7071, 0.7071) of unit circle and r.
Hence the value of sin 7pi/4 = y = 0.7071 (approx)
☛ Also Check:
Examples Using Sin 7pi/4

Example 1: Find the value of 5 sin(7pi/4)/7 cos(5pi/4).
Solution:
Using trigonometric identities, we know, sin(7pi/4) = cos(pi/2  7pi/4) = cos(5pi/4).
⇒ sin(7pi/4) = cos(5pi/4)
⇒ Value of 5 sin(7pi/4)/7 cos(5pi/4) = 5/7 
Example 2: Find the value of 2 × (sin(7pi/8) cos(7pi/8)). [Hint: Use sin 7pi/4 = 0.7071]
Solution:
Using the sin 2a formula,
2 sin(7pi/8) cos(7pi/8) = sin(2 × 7pi/8) = sin 7pi/4
∵ sin 7pi/4 = 0.7071
⇒ 2 × (sin(7pi/8) cos(7pi/8)) = 0.7071 
Example 3: Using the value of sin 7pi/4, solve: (1cos²(7pi/4)).
Solution:
We know, (1cos²(7pi/4)) = (sin²(7pi/4)) = 0.5
⇒ (1cos²(7pi/4)) = 0.5
FAQs on Sin 7pi/4
What is Sin 7pi/4?
Sin 7pi/4 is the value of sine trigonometric function for an angle equal to 7pi/4 radians. The value of sin 7pi/4 is (1/√2) or 0.7071 (approx).
How to Find Sin 7pi/4 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 7π/4 can be given in terms of other trigonometric functions as:
 ± √(1cos²(7pi/4))
 ± tan(7pi/4)/√(1 + tan²(7pi/4))
 ± 1/√(1 + cot²(7pi/4))
 ± √(sec²(7pi/4)  1)/sec(7pi/4)
 1/cosec(7pi/4)
☛ Also check: trigonometry table
What is the Exact Value of sin 7pi/4?
The exact value of sin 7pi/4 can be given accurately up to 8 decimal places as 0.70710678 and (1/√2) in fraction.
How to Find the Value of Sin 7pi/4?
The value of sin 7pi/4 can be calculated by constructing an angle of 7π/4 radians with the xaxis, and then finding the coordinates of the corresponding point (0.7071, 0.7071) on the unit circle. The value of sin 7pi/4 is equal to the ycoordinate (0.7071). ∴ sin 7pi/4 = 0.7071.
What is the Value of Sin 7pi/4 in Terms of Cot 7pi/4?
We can represent the sine function in terms of the cotangent function using trig identities, sin 7pi/4 can be written as 1/√(1 + cot²(7pi/4)). Here, the value of cot 7pi/4 is equal to 1.
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