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 x-axis.
- The tan of 7pi/8 equals the y-coordinate(0.3827) divided by the x-coordinate(-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:
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 x-axis, 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 y-coordinate(0.3827) divided by the x-coordinate (-0.9239). ∴ tan 7pi/8 = -0.4142