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Tan pi/4
The value of tan pi/4 is 1. Tan pi/4 radians in degrees is written as tan ((π/4) × 180°/π), i.e., tan (45°). In this article, we will discuss the methods to find the value of tan pi/4 with examples.
 Tan pi/4: 1
 Tan (pi/4): 1
 Tan pi/4 in degrees: tan (45°)
What is the Value of Tan pi/4?
The value of tan pi/4 is 1. Tan pi/4 can also be expressed using the equivalent of the given angle (pi/4) in degrees (45°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/4 radians = pi/4 × (180°/pi) = 45° or 45 degrees
∴ tan pi/4 = tan π/4 = tan(45°) = 1
Explanation:
For tan pi/4, the angle pi/4 lies between 0 and pi/2 (First Quadrant). Since tangent function is positive in the first quadrant, thus tan pi/4 value = 1
Since the tangent function is a periodic function, we can represent tan pi/4 as, tan pi/4 = tan(pi/4 + n × pi), n ∈ Z.
⇒ tan pi/4 = tan 5pi/4 = tan 9pi/4 , and so on.
Note: Since, tangent is an odd function, the value of tan(pi/4) = tan(pi/4).
Methods to Find Value of Tan pi/4
The tangent function is positive in the 1st quadrant. The value of tan pi/4 is given as 1. We can find the value of tan pi/4 by:
 Using Trigonometric Functions
 Using Unit Circle
Tan pi/4 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan pi/4 as:
 sin(pi/4)/cos(pi/4)
 ± sin(pi/4)/√(1  sin²(pi/4))
 ± √(1  cos²(pi/4))/cos(pi/4)
 ± 1/√(cosec²(pi/4)  1)
 ± √(sec²(pi/4)  1)
 1/cot(pi/4)
Note: Since pi/4 lies in the 1st Quadrant, the final value of tan pi/4 will be positive.
We can use trigonometric identities to represent tan pi/4 as,
 cot(pi/2  pi/4) = cot pi/4
 cot(pi/2 + pi/4) = cot 3pi/4
 tan (pi  pi/4) = tan 3pi/4
Tan pi/4 Using Unit Circle
To find the value of tan π/4 using the unit circle:
 Rotate ‘r’ anticlockwise to form pi/4 angle with the positive xaxis.
 The tan of pi/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 pi/4 = y/x = 1
☛ Also Check:
Examples Using Tan pi/4

Example 1: Find the value of tan pi/4 if cot pi/4 is 1.
Solution:
Since, tan pi/4 = 1/cot(pi/4)
⇒ tan pi/4 = 1/1 = 1 
Example 2: Find the value of (2 sin (pi/8) cos (pi/8) sec (pi/4)). [Hint: Use tan pi/4 = 1]
Solution:
Using sin 2a formula,
2 sin (pi/8) cos (pi/8) = sin (2 × pi/8) = sin pi/4
⇒ 2 sin (pi/8) cos (pi/8) sec(pi/4) = sin(pi/4) sec(pi/4)
= sin(pi/4)/cos(pi/4) = tan pi/4
⇒ (2 sin (pi/8) cos (pi/8) sec(pi/4)) = 1 
Example 3: Simplify: 3 (tan(pi/4)/cot(pi/4))
Solution:
We know tan pi/4 = cot pi/4
⇒ 3 tan(pi/4)/cot(pi/4) = 3 tan(pi/4)/tan(pi/4)
= 3(1) = 3
FAQs on Tan pi/4
What is Tan pi/4?
Tan pi/4 is the value of tangent trigonometric function for an angle equal to π/4 radians. The value of tan pi/4 is 1.
How to Find Tan pi/4 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan pi/4 can be given in terms of other trigonometric functions as:
 sin(pi/4)/cos(pi/4)
 ± sin(pi/4)/√(1  sin²(pi/4))
 ± √(1  cos²(pi/4))/cos(pi/4)
 ± 1/√(cosec²(pi/4)  1)
 ± √(sec²(pi/4)  1)
 1/cot(pi/4)
☛ Also check: trigonometry table
What is the Value of Tan pi/4 in Terms of Cos pi/4?
We know, using trig identities, we can write tan pi/4 as √(1  cos²(pi/4))/cos pi/4. Here, the value of cos pi/4 is equal to 0.707106.
How to Find the Value of Tan pi/4?
The value of tan pi/4 can be calculated by constructing an angle of π/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 pi/4 is equal to the ycoordinate(0.7071) divided by the xcoordinate (0.7071). ∴ tan pi/4 = 1
What is the Exact Value of tan pi/4?
The exact value of tan pi/4 is 1.
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