Cos 7pi/4
The value of cos 7pi/4 is 0.7071067. . .. Cos 7pi/4 radians in degrees is written as cos ((7π/4) × 180°/π), i.e., cos (315°). In this article, we will discuss the methods to find the value of cos 7pi/4 with examples.
- Cos 7pi/4: 1/√2
- Cos 7pi/4 in decimal: 0.7071067. . .
- Cos (-7pi/4): 0.7071067. . . or 1/√2
- Cos 7pi/4 in degrees: cos (315°)
What is the Value of Cos 7pi/4?
The value of cos 7pi/4 in decimal is 0.707106781. . .. Cos 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
∴ cos 7pi/4 = cos 7π/4 = cos(315°) = 1/√2 or 0.7071067. . .
Explanation:
For cos 7pi/4, the angle 7pi/4 lies between 3pi/2 and 2pi (Fourth Quadrant). Since cosine function is positive in the fourth quadrant, thus cos 7pi/4 value = 1/√2 or 0.7071067. . .
Since the cosine function is a periodic function, we can represent cos 7pi/4 as, cos 7pi/4 = cos(7pi/4 + n × 2pi), n ∈ Z.
⇒ cos 7pi/4 = cos 15pi/4 = cos 23pi/4 , and so on.
Note: Since, cosine is an even function, the value of cos(-7pi/4) = cos(7pi/4).
Methods to Find Value of Cos 7pi/4
The cosine function is positive in the 4th quadrant. The value of cos 7pi/4 is given as 0.70710. . .. We can find the value of cos 7pi/4 by:
- Using Trigonometric Functions
- Using Unit Circle
Cos 7pi/4 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos 7pi/4 as:
- ± √(1-sin²(7pi/4))
- ± 1/√(1 + tan²(7pi/4))
- ± cot(7pi/4)/√(1 + cot²(7pi/4))
- ±√(cosec²(7pi/4) - 1)/cosec(7pi/4)
- 1/sec(7pi/4)
Note: Since 7pi/4 lies in the 4th Quadrant, the final value of cos 7pi/4 will be positive.
We can use trigonometric identities to represent cos 7pi/4 as,
- -cos(pi - 7pi/4) = -cos(-3pi/4)
- -cos(pi + 7pi/4) = -cos 11pi/4
- sin(pi/2 + 7pi/4) = sin 9pi/4
- sin(pi/2 - 7pi/4) = sin(-5pi/4)
Cos 7pi/4 Using Unit Circle
To find the value of cos 7π/4 using the unit circle:
- Rotate ‘r’ anticlockwise to form 7pi/4 angle with the positive x-axis.
- The cos of 7pi/4 equals the x-coordinate(0.7071) of the point of intersection (0.7071, -0.7071) of unit circle and r.
Hence the value of cos 7pi/4 = x = 0.7071 (approx)
☛ Also Check:
FAQs on Cos 7pi/4
What is Cos 7pi/4?
Cos 7pi/4 is the value of cosine trigonometric function for an angle equal to 7π/4 radians. The value of cos 7pi/4 is 1/√2 or 0.7071 (approx)
What is the Value of Cos 7pi/4 in Terms of Cot 7pi/4?
We can represent the cosine function in terms of the cotangent function using trig identities, cos 7pi/4 can be written as -cot(7pi/4)/√(1 + cot²(7pi/4)). Here, the value of cot 7pi/4 is equal to -1.
How to Find Cos 7pi/4 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos 7pi/4 can be given in terms of other trigonometric functions as:
- ± √(1-sin²(7pi/4))
- ± 1/√(1 + tan²(7pi/4))
- ± cot(7pi/4)/√(1 + cot²(7pi/4))
- ±√(cosec²(7pi/4) - 1)/cosec(7pi/4)
- 1/sec(7pi/4)
☛ Also check: trigonometric table
How to Find the Value of Cos 7pi/4?
The value of cos 7pi/4 can be calculated by constructing an angle of 7π/4 radians with the x-axis, and then finding the coordinates of the corresponding point (0.7071, -0.7071) on the unit circle. The value of cos 7pi/4 is equal to the x-coordinate (0.7071). ∴ cos 7pi/4 = 0.7071.
What is the Exact Value of cos 7pi/4?
The exact value of cos 7pi/4 can be given accurately up to 8 decimal places as 0.70710678 and 1/√2 in fraction.