Tan 225 Degrees

The value of tan 225 degrees is 1. Tan 225 degrees in radians is written as tan (225° × π/180°), i.e., tan (5π/4) or tan (3.926990. . .). In this article, we will discuss the methods to find the value of tan 225 degrees with examples.

• Tan 225°: 1
• Tan (-225 degrees): -1
• Tan 225° in radians: tan (5π/4) or tan (3.9269908 . . .)

What is the Value of Tan 225 Degrees?

The value of tan 225 degrees is 1. Tan 225 degrees can also be expressed using the equivalent of the given angle (225 degrees) in radians (3.92699 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 225 degrees = 225° × (π/180°) rad = 5π/4 or 3.9269 . . .
∴ tan 225° = tan(3.9269) = 1

Explanation:

For tan 225 degrees, the angle 225° lies between 180° and 270° (Third Quadrant). Since tangent function is positive in the third quadrant, thus tan 225° value = 1
Since the tangent function is a periodic function, we can represent tan 225° as, tan 225 degrees = tan(225° + n × 180°), n ∈ Z.
⇒ tan 225° = tan 405° = tan 585°, and so on.
Note: Since, tangent is an odd function, the value of tan(-225°) = -tan(225°).

Methods to Find Value of Tan 225 Degrees

The tangent function is positive in the 3rd quadrant. The value of tan 225° is given as 1. We can find the value of tan 225 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 225° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 225 degrees as:

• sin(225°)/cos(225°)
• ± sin 225°/√(1 - sin²(225°))
• ± √(1 - cos²(225°))/cos 225°
• ± 1/√(cosec²(225°) - 1)
• ± √(sec²(225°) - 1)
• 1/cot 225°

Note: Since 225° lies in the 3rd Quadrant, the final value of tan 225° will be positive.

We can use trigonometric identities to represent tan 225° as,

• cot(90° - 225°) = cot(-135°)
• -cot(90° + 225°) = -cot 315°
• -tan (180° - 225°) = -tan(-45°)

Tan 225 Degrees Using Unit Circle

To find the value of tan 225 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 225° angle with the positive x-axis.
• The tan of 225 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 225° = y/x = 1

☛ Also Check:

• tan 120 degrees
• tan 90 degrees
• tan 1 degrees
• tan 480 degrees
• tan 8 degrees
• tan 27 degrees

FAQs on Tan 225 Degrees

What is Tan 225 Degrees?

Tan 225 degrees is the value of tangent trigonometric function for an angle equal to 225 degrees. The value of tan 225° is 1.

What is the Value of Tan 225° in Terms of Sec 225°?

We can represent the tangent function in terms of the secant function using trig identities, tan 225° can be written as √(sec²(225°) - 1). Here, the value of sec 225° is equal to -1.4142.

What is the Value of Tan 225 Degrees in Terms of Cot 225°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 225° as 1/cot(225°). The value of cot 225° is equal to 1.

How to Find the Value of Tan 225 Degrees?

The value of tan 225 degrees can be calculated by constructing an angle of 225° 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 225° is equal to the y-coordinate(-0.7071) divided by the x-coordinate (-0.7071). ∴ tan 225° = 1

How to Find Tan 225° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 225° can be given in terms of other trigonometric functions as:

• sin(225°)/cos(225°)
• ± sin 225°/√(1 - sin²(225°))
• ± √(1 - cos²(225°))/cos 225°
• ± 1/√(cosec²(225°) - 1)
• ± √(sec²(225°) - 1)
• 1/cot 225°

☛ Also check: trigonometric table