Tan 23 Degrees

The value of tan 23 degrees is 0.4244748. . .. Tan 23 degrees in radians is written as tan (23° × π/180°), i.e., tan (0.401425. . .). In this article, we will discuss the methods to find the value of tan 23 degrees with examples.

• Tan 23° in decimal: 0.4244748. . .
• Tan (-23 degrees): -0.4244748. . .
• Tan 23° in radians: tan (0.4014257 . . .)

What is the Value of Tan 23 Degrees?

The value of tan 23 degrees in decimal is 0.424474816. . .. Tan 23 degrees can also be expressed using the equivalent of the given angle (23 degrees) in radians (0.40142 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 23 degrees = 23° × (π/180°) rad = 0.4014 . . .
∴ tan 23° = tan(0.4014) = 0.4244748. . .

Explanation:

For tan 23 degrees, the angle 23° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 23° value = 0.4244748. . .
Since the tangent function is a periodic function, we can represent tan 23° as, tan 23 degrees = tan(23° + n × 180°), n ∈ Z.
⇒ tan 23° = tan 203° = tan 383°, and so on.
Note: Since, tangent is an odd function, the value of tan(-23°) = -tan(23°).

Methods to Find Value of Tan 23 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 23° is given as 0.42447. . .. We can find the value of tan 23 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 23 Degrees Using Unit Circle

To find the value of tan 23 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 23° angle with the positive x-axis.
• The tan of 23 degrees equals the y-coordinate(0.3907) divided by x-coordinate(0.9205) of the point of intersection (0.9205, 0.3907) of unit circle and r.

Hence the value of tan 23° = y/x = 0.4245 (approx).

Tan 23° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 23 degrees as:

• sin(23°)/cos(23°)
• ± sin 23°/√(1 - sin²(23°))
• ± √(1 - cos²(23°))/cos 23°
• ± 1/√(cosec²(23°) - 1)
• ± √(sec²(23°) - 1)
• 1/cot 23°

Note: Since 23° lies in the 1st Quadrant, the final value of tan 23° will be positive.

We can use trigonometric identities to represent tan 23° as,

• cot(90° - 23°) = cot 67°
• -cot(90° + 23°) = -cot 113°
• -tan (180° - 23°) = -tan 157°

☛ Also Check:

• tan 45 degrees
• tan 180 degrees
• tan 0 degrees
• tan 78 degrees
• tan 145 degrees
• tan 57 degrees

FAQs on Tan 23 Degrees

What is Tan 23 Degrees?

Tan 23 degrees is the value of tangent trigonometric function for an angle equal to 23 degrees. The value of tan 23° is 0.4245 (approx).

How to Find Tan 23° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 23° can be given in terms of other trigonometric functions as:

• sin(23°)/cos(23°)
• ± sin 23°/√(1 - sin²(23°))
• ± √(1 - cos²(23°))/cos 23°
• ± 1/√(cosec²(23°) - 1)
• ± √(sec²(23°) - 1)
• 1/cot 23°

☛ Also check: trigonometric table

What is the Value of Tan 23 Degrees in Terms of Cot 23°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 23° as 1/cot(23°). The value of cot 23° is equal to 2.35585.

What is the Exact Value of tan 23 Degrees?

The exact value of tan 23 degrees can be given accurately up to 8 decimal places as 0.42447481.

How to Find the Value of Tan 23 Degrees?

The value of tan 23 degrees can be calculated by constructing an angle of 23° with the x-axis, and then finding the coordinates of the corresponding point (0.9205, 0.3907) on the unit circle. The value of tan 23° is equal to the y-coordinate(0.3907) divided by the x-coordinate (0.9205). ∴ tan 23° = 0.4245