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Tan 7pi/8
The value of tan 7pi/8 is 0.4142135. . .. Tan 7pi/8 radians in degrees is written as tan ((7π/8) × 180°/π), i.e., tan (157.5°). In this article, we will discuss the methods to find the value of tan 7pi/8 with examples.
 Tan 7pi/8 in decimal: 0.4142135. . .
 Tan (7pi/8): 0.4142135. . .
 Tan 7pi/8 in degrees: tan (157.5°)
What is the Value of Tan 7pi/8?
The value of tan 7pi/8 in decimal is 0.414213562. . .. Tan 7pi/8 can also be expressed using the equivalent of the given angle (7pi/8) in degrees (157.5°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi/8 radians = 7pi/8 × (180°/pi) = 157.5° or 157.5 degrees
∴ tan 7pi/8 = tan 7π/8 = tan(157.5°) = 0.4142135. . .
Explanation:
For tan 7pi/8, the angle 7pi/8 lies between pi/2 and pi (Second Quadrant). Since tangent function is negative in the second quadrant, thus tan 7pi/8 value = 0.4142135. . .
Since the tangent function is a periodic function, we can represent tan 7pi/8 as, tan 7pi/8 = tan(7pi/8 + n × pi), n ∈ Z.
⇒ tan 7pi/8 = tan 15pi/8 = tan 23pi/8 , and so on.
Note: Since, tangent is an odd function, the value of tan(7pi/8) = tan(7pi/8).
Methods to Find Value of Tan 7pi/8
The tangent function is negative in the 2nd quadrant. The value of tan 7pi/8 is given as 0.41421. . .. We can find the value of tan 7pi/8 by:
 Using Trigonometric Functions
 Using Unit Circle
Tan 7pi/8 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 7pi/8 as:
 sin(7pi/8)/cos(7pi/8)
 ± sin(7pi/8)/√(1  sin²(7pi/8))
 ± √(1  cos²(7pi/8))/cos(7pi/8)
 ± 1/√(cosec²(7pi/8)  1)
 ± √(sec²(7pi/8)  1)
 1/cot(7pi/8)
Note: Since 7pi/8 lies in the 2nd Quadrant, the final value of tan 7pi/8 will be negative.
We can use trigonometric identities to represent tan 7pi/8 as,
 cot(pi/2  7pi/8) = cot(3pi/8)
 cot(pi/2 + 7pi/8) = cot 11pi/8
 tan (pi  7pi/8) = tan pi/8
Tan 7pi/8 Using Unit Circle
To find the value of tan 7π/8 using the unit circle:
 Rotate ‘r’ anticlockwise to form 7pi/8 angle with the positive xaxis.
 The tan of 7pi/8 equals the ycoordinate(0.3827) divided by the xcoordinate(0.9239) of the point of intersection (0.9239, 0.3827) of unit circle and r.
Hence the value of tan 7pi/8 = y/x = 0.4142 (approx)
☛ Also Check:
Examples Using Tan 7pi/8

Example 1: Using the value of tan 7pi/8, solve: (sec²(7pi/8)  1).
Solution:
We know, (sec²(7pi/8)  1) = (tan²(7pi/8)) = 0.1716
⇒ (sec²(7pi/8)  1) = 0.1716 
Example 2: Simplify: 4 (tan(7pi/8)/cot(3pi/8))
Solution:
We know tan 7pi/8 = cot(3pi/8)
⇒ 4 tan(7pi/8)/cot(3pi/8) = 4 tan(7pi/8)/tan(7pi/8)
= 4(1) = 4 
Example 3: Find the value of tan 7pi/8 if cot 7pi/8 is 2.4142.
Solution:
Since, tan 7pi/8 = 1/cot(7pi/8)
⇒ tan 7pi/8 = 1/(2.4142) = 0.4142
FAQs on Tan 7pi/8
What is Tan 7pi/8?
Tan 7pi/8 is the value of tangent trigonometric function for an angle equal to 7π/8 radians. The value of tan 7pi/8 is 0.4142 (approx).
What is the Exact Value of tan 7pi/8?
The exact value of tan 7pi/8 can be given accurately up to 8 decimal places as 0.41421356.
How to Find Tan 7pi/8 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 7pi/8 can be given in terms of other trigonometric functions as:
 sin(7pi/8)/cos(7pi/8)
 ± sin(7pi/8)/√(1  sin²(7pi/8))
 ± √(1  cos²(7pi/8))/cos(7pi/8)
 ± 1/√(cosec²(7pi/8)  1)
 ± √(sec²(7pi/8)  1)
 1/cot(7pi/8)
☛ Also check: trigonometric table
What is the Value of Tan 7pi/8 in Terms of Cot 7pi/8?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 7pi/8 as 1/cot(7pi/8). The value of cot 7pi/8 is equal to 2.41421.
How to Find the Value of Tan 7pi/8?
The value of tan 7pi/8 can be calculated by constructing an angle of 7π/8 radians with the xaxis, and then finding the coordinates of the corresponding point (0.9239, 0.3827) on the unit circle. The value of tan 7pi/8 is equal to the ycoordinate(0.3827) divided by the xcoordinate (0.9239). ∴ tan 7pi/8 = 0.4142
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