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 x-axis.
• The tan of 7pi/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 7pi/4 = y/x = -1

☛ Also Check:

• sec pi/2
• sin 5pi/12
• csc pi/3
• tan 5pi/4
• tan pi/4
• cos pi/2

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 x-axis, 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 y-coordinate(-0.7071) divided by the x-coordinate (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