Tan 315 Degrees

The value of tan 315 degrees is -1. Tan 315 degrees in radians is written as tan (315° × π/180°), i.e., tan (7π/4) or tan (5.497787. . .). In this article, we will discuss the methods to find the value of tan 315 degrees with examples.

• Tan 315°: -1
• Tan (-315 degrees): 1
• Tan 315° in radians: tan (7π/4) or tan (5.4977871 . . .)

What is the Value of Tan 315 Degrees?

The value of tan 315 degrees is -1. Tan 315 degrees can also be expressed using the equivalent of the given angle (315 degrees) in radians (5.49778 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 315 degrees = 315° × (π/180°) rad = 7π/4 or 5.4977 . . .
∴ tan 315° = tan(5.4977) = -1

Explanation:

For tan 315 degrees, the angle 315° lies between 270° and 360° (Fourth Quadrant). Since tangent function is negative in the fourth quadrant, thus tan 315° value = -1
Since the tangent function is a periodic function, we can represent tan 315° as, tan 315 degrees = tan(315° + n × 180°), n ∈ Z.
⇒ tan 315° = tan 495° = tan 675°, and so on.
Note: Since, tangent is an odd function, the value of tan(-315°) = -tan(315°).

Methods to Find Value of Tan 315 Degrees

The tangent function is negative in the 4th quadrant. The value of tan 315° is given as -1. We can find the value of tan 315 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 315° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 315 degrees as:

• sin(315°)/cos(315°)
• ± sin 315°/√(1 - sin²(315°))
• ± √(1 - cos²(315°))/cos 315°
• ± 1/√(cosec²(315°) - 1)
• ± √(sec²(315°) - 1)
• 1/cot 315°

Note: Since 315° lies in the 4th Quadrant, the final value of tan 315° will be negative.

We can use trigonometric identities to represent tan 315° as,

• cot(90° - 315°) = cot(-225°)
• -cot(90° + 315°) = -cot 405°
• -tan (180° - 315°) = -tan(-135°)

Tan 315 Degrees Using Unit Circle

To find the value of tan 315 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 315° angle with the positive x-axis.
• The tan of 315 degrees equals the y-coordinate(-0.7071) divided by x-coordinate(0.7071) of the point of intersection (0.7071, -0.7071) of unit circle and r.

Hence the value of tan 315° = y/x = -1

☛ Also Check:

• tan 50 degrees
• tan 3 degrees
• tan 90 degrees
• tan 570 degrees
• tan 46 degrees
• tan 67 degrees

FAQs on Tan 315 Degrees

What is Tan 315 Degrees?

Tan 315 degrees is the value of tangent trigonometric function for an angle equal to 315 degrees. The value of tan 315° is -1.

What is the Value of Tan 315 Degrees in Terms of Cos 315°?

We know, using trig identities, we can write tan 315° as -√(1 - cos²(315°))/cos 315°. Here, the value of cos 315° is equal to 0.707106.

How to Find the Value of Tan 315 Degrees?

The value of tan 315 degrees can be calculated by constructing an angle of 315° 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 315° is equal to the y-coordinate(-0.7071) divided by the x-coordinate (0.7071). ∴ tan 315° = -1

How to Find Tan 315° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 315° can be given in terms of other trigonometric functions as:

• sin(315°)/cos(315°)
• ± sin 315°/√(1 - sin²(315°))
• ± √(1 - cos²(315°))/cos 315°
• ± 1/√(cosec²(315°) - 1)
• ± √(sec²(315°) - 1)
• 1/cot 315°

☛ Also check: trigonometric table

What is the Value of Tan 315° in Terms of Cosec 315°?

Since the tangent function can be represented using the cosecant function, we can write tan 315° as -1/√(cosec²(315°) - 1). The value of cosec 315° is equal to -1.41421.