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Tan 7pi/4
The value of tan 7pi/4 is 1. Tan 7pi/4 radians in degrees is written as tan ((7π/4) × 180°/π), i.e., tan (315°). In this article, we will discuss the methods to find the value of tan 7pi/4 with examples.
 Tan 7pi/4: 1
 Tan (7pi/4): 1
 Tan 7pi/4 in degrees: tan (315°)
What is the Value of Tan 7pi/4?
The value of tan 7pi/4 is 1. Tan 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
∴ tan 7pi/4 = tan 7π/4 = tan(315°) = 1
Explanation:
For tan 7pi/4, the angle 7pi/4 lies between 3pi/2 and 2pi (Fourth Quadrant). Since tangent function is negative in the fourth quadrant, thus tan 7pi/4 value = 1
Since the tangent function is a periodic function, we can represent tan 7pi/4 as, tan 7pi/4 = tan(7pi/4 + n × pi), n ∈ Z.
⇒ tan 7pi/4 = tan 11pi/4 = tan 15pi/4 , and so on.
Note: Since, tangent is an odd function, the value of tan(7pi/4) = tan(7pi/4).
Methods to Find Value of Tan 7pi/4
The tangent function is negative in the 4th quadrant. The value of tan 7pi/4 is given as 1. We can find the value of tan 7pi/4 by:
 Using Trigonometric Functions
 Using Unit Circle
Tan 7pi/4 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 7pi/4 as:
 sin(7pi/4)/cos(7pi/4)
 ± sin(7pi/4)/√(1  sin²(7pi/4))
 ± √(1  cos²(7pi/4))/cos(7pi/4)
 ± 1/√(cosec²(7pi/4)  1)
 ± √(sec²(7pi/4)  1)
 1/cot(7pi/4)
Note: Since 7pi/4 lies in the 4th Quadrant, the final value of tan 7pi/4 will be negative.
We can use trigonometric identities to represent tan 7pi/4 as,
 cot(pi/2  7pi/4) = cot(5pi/4)
 cot(pi/2 + 7pi/4) = cot 9pi/4
 tan (pi  7pi/4) = tan(3pi/4)
Tan 7pi/4 Using Unit Circle
To find the value of tan 7π/4 using the unit circle:
 Rotate ‘r’ anticlockwise to form 7pi/4 angle with the positive xaxis.
 The tan of 7pi/4 equals the ycoordinate(0.7071) divided by the xcoordinate(0.7071) of the point of intersection (0.7071, 0.7071) of unit circle and r.
Hence the value of tan 7pi/4 = y/x = 1
☛ Also Check:
Examples Using Tan 7pi/4

Example 1: Using the value of tan 7pi/4, solve: (sec²(7pi/4)  1).
Solution:
We know, (sec²(7pi/4)  1) = (tan²(7pi/4)) = 1
⇒ (sec²(7pi/4)  1) = 1 
Example 2: Find the value of 2 tan(7pi/8)/(1  tan²(7pi/8)). [Hint: Use tan 7pi/4 = 1]
Solution:
Using the tan 2a formula,
2 tan(7pi/8)/(1  tan²(7pi/8)) = tan(2 × 7pi/8) = tan 7pi/4
∵ tan 7pi/4 = 1
⇒ 2 tan(7pi/8)/(1  tan²(7pi/8)) = 1 
Example 3: Simplify: 5 (tan(7pi/4)/cot(5pi/4))
Solution:
We know tan 7pi/4 = cot(5pi/4)
⇒ 5 tan(7pi/4)/cot(5pi/4) = 5 tan(7pi/4)/tan(7pi/4)
= 5(1) = 5
FAQs on Tan 7pi/4
What is Tan 7pi/4?
Tan 7pi/4 is the value of tangent trigonometric function for an angle equal to 7π/4 radians. The value of tan 7pi/4 is 1.
What is the Value of Tan 7pi/4 in Terms of Cosec 7pi/4?
Since the tangent function can be represented using the cosecant function, we can write tan 7pi/4 as 1/√(cosec²(7pi/4)  1). The value of cosec 7pi/4 is equal to 1.41421.
What is the Value of Tan 7pi/4 in Terms of Cot 7pi/4?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 7pi/4 as 1/cot(7pi/4). The value of cot 7pi/4 is equal to 1.
How to Find the Value of Tan 7pi/4?
The value of tan 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 tan 7pi/4 is equal to the ycoordinate(0.7071) divided by the xcoordinate (0.7071). ∴ tan 7pi/4 = 1
How to Find Tan 7pi/4 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 7pi/4 can be given in terms of other trigonometric functions as:
 sin(7pi/4)/cos(7pi/4)
 ± sin(7pi/4)/√(1  sin²(7pi/4))
 ± √(1  cos²(7pi/4))/cos(7pi/4)
 ± 1/√(cosec²(7pi/4)  1)
 ± √(sec²(7pi/4)  1)
 1/cot(7pi/4)
☛ Also check: trigonometric table
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