Tan 45 Degrees

The value of tan 45 degrees is 1. Tan 45 degrees in radians is written as tan (45° × π/180°), i.e., tan (π/4) or tan (0.785398. . .). In this article, we will discuss the methods to find the value of tan 45 degrees with examples.

• Tan 45°: 1
• Tan (-45 degrees): -1
• Tan 45° in radians: tan (π/4) or tan (0.7853981 . . .)

What is the Value of Tan 45 Degrees?

The value of tan 45 degrees is 1. Tan 45 degrees can also be expressed using the equivalent of the given angle (45 degrees) in radians (0.78539 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 45 degrees = 45° × (π/180°) rad = π/4 or 0.7853 . . .
∴ tan 45° = tan(0.7853) = 1

Explanation:

For tan 45 degrees, the angle 45° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 45° value = 1
Since the tangent function is a periodic function, we can represent tan 45° as, tan 45 degrees = tan(45° + n × 180°), n ∈ Z.
⇒ tan 45° = tan 225° = tan 405°, and so on.
Note: Since, tangent is an odd function, the value of tan(-45°) = -tan(45°).

Methods to Find Value of Tan 45 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 45° is given as 1. We can find the value of tan 45 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 45° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 45 degrees as:

• sin(45°)/cos(45°)
• ± sin 45°/√(1 - sin²(45°))
• ± √(1 - cos²(45°))/cos 45°
• ± 1/√(cosec²(45°) - 1)
• ± √(sec²(45°) - 1)
• 1/cot 45°

Note: Since 45° lies in the 1st Quadrant, the final value of tan 45° will be positive.

We can use trigonometric identities to represent tan 45° as,

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

Tan 45 Degrees Using Unit Circle

To find the value of tan 45 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 45° angle with the positive x-axis.
• The tan of 45 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 45° = y/x = 1

☛ Also Check:

• tan 30 degrees
• tan 360 degrees
• tan 12 degrees
• tan 390 degrees
• tan 38 degrees
• tan 140 degrees

FAQs on Tan 45 Degrees

What is Tan 45 Degrees?

Tan 45 degrees is the value of tangent trigonometric function for an angle equal to 45 degrees. The value of tan 45° is 1.

How to Find Tan 45° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 45° can be given in terms of other trigonometric functions as:

• sin(45°)/cos(45°)
• ± sin 45°/√(1 - sin²(45°))
• ± √(1 - cos²(45°))/cos 45°
• ± 1/√(cosec²(45°) - 1)
• ± √(sec²(45°) - 1)
• 1/cot 45°

☛ Also check: trigonometric table

How to Find the Value of Tan 45 Degrees?

The value of tan 45 degrees can be calculated by constructing an angle of 45° 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 45° is equal to the y-coordinate(0.7071) divided by the x-coordinate (0.7071). ∴ tan 45° = 1

What is the Value of Tan 45 Degrees in Terms of Cot 45°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 45° as 1/cot(45°). The value of cot 45° is equal to 1.

What is the Exact Value of tan 45 Degrees?

The exact value of tan 45 degrees is 1.