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 x-axis.
• The tan of pi/4 equals the y-coordinate(0.7071) divided by the x-coordinate(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:

• cos pi/2
• sin 11pi/6
• cot pi/3
• cos pi/12
• sin 7pi/6
• cot 5pi/4

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 x-axis, 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 y-coordinate(0.7071) divided by the x-coordinate (0.7071). ∴ tan pi/4 = 1

What is the Exact Value of tan pi/4?

The exact value of tan pi/4 is 1.