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Tan 21 Degrees

The value of tan 21 degrees is 0.3838640. . .. Tan 21 degrees in radians is written as tan (21° × π/180°), i.e., tan (7π/60) or tan (0.366519. . .). In this article, we will discuss the methods to find the value of tan 21 degrees with examples.

Tan 21° in decimal: 0.3838640. . .
Tan (-21 degrees): -0.3838640. . .
Tan 21° in radians: tan (7π/60) or tan (0.3665191 . . .)

What is the Value of Tan 21 Degrees?

The value of tan 21 degrees in decimal is 0.383864035. . .. Tan 21 degrees can also be expressed using the equivalent of the given angle (21 degrees) in radians (0.36651 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 21 degrees = 21° × (π/180°) rad = 7π/60 or 0.3665 . . .
∴ tan 21° = tan(0.3665) = 0.3838640. . .

Explanation:

For tan 21 degrees, the angle 21° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 21° value = 0.3838640. . .
Since the tangent function is a periodic function, we can represent tan 21° as, tan 21 degrees = tan(21° + n × 180°), n ∈ Z.
⇒ tan 21° = tan 201° = tan 381°, and so on.
Note: Since, tangent is an odd function, the value of tan(-21°) = -tan(21°).

Methods to Find Value of Tan 21 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 21° is given as 0.38386. . .. We can find the value of tan 21 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 21° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 21 degrees as:

sin(21°)/cos(21°)
± sin 21°/√(1 - sin²(21°))
± √(1 - cos²(21°))/cos 21°
± 1/√(cosec²(21°) - 1)
± √(sec²(21°) - 1)
1/cot 21°

Note: Since 21° lies in the 1st Quadrant, the final value of tan 21° will be positive.

We can use trigonometric identities to represent tan 21° as,

cot(90° - 21°) = cot 69°
-cot(90° + 21°) = -cot 111°
-tan (180° - 21°) = -tan 159°

Tan 21 Degrees Using Unit Circle

To find the value of tan 21 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 21° angle with the positive x-axis.
The tan of 21 degrees equals the y-coordinate(0.3584) divided by x-coordinate(0.9336) of the point of intersection (0.9336, 0.3584) of unit circle and r.

Hence the value of tan 21° = y/x = 0.3839 (approx).

☛ Also Check:

Examples Using Tan 21 Degrees

Example 1: Using the value of tan 21°, solve: (sec²(21°) - 1).

Solution:
We know, (sec²(21°) - 1) = (tan²(21°)) = 0.1474
⇒ (sec²(21°) - 1) = 0.1474
Example 2: Find the value of (2 sin (10.5°) cos (10.5°) sec (21°)). [Hint: Use tan 21° = 0.3839]

Solution:

Using sin 2a formula,
2 sin (10.5°) cos (10.5°) = sin (2 × 10.5°) = sin 21°
⇒ 2 sin (10.5°) cos (10.5°) sec(21°) = sin 21° sec 21°
= sin 21°/cos 21° = tan 21°
⇒ (2 sin (10.5°) cos (10.5°) sec(21°)) = 0.3839
Example 3: Find the value of tan 21° if cot 21° is 2.6050.

Solution:
Since, tan 21° = 1/cot 21°
⇒ tan 21° = 1/2.6050 = 0.3839

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FAQs on Tan 21 Degrees

What is Tan 21 Degrees?

Tan 21 degrees is the value of tangent trigonometric function for an angle equal to 21 degrees. The value of tan 21° is 0.3839 (approx).

What is the Value of Tan 21 Degrees in Terms of Cot 21°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 21° as 1/cot(21°). The value of cot 21° is equal to 2.60508.

How to Find Tan 21° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 21° can be given in terms of other trigonometric functions as:

sin(21°)/cos(21°)
± sin 21°/√(1 - sin²(21°))
± √(1 - cos²(21°))/cos 21°
± 1/√(cosec²(21°) - 1)
± √(sec²(21°) - 1)
1/cot 21°

☛ Also check: trigonometric table

What is the Value of Tan 21° in Terms of Sec 21°?

We can represent the tangent function in terms of the secant function using trig identities, tan 21° can be written as √(sec²(21°) - 1). Here, the value of sec 21° is equal to 1.0711.

How to Find the Value of Tan 21 Degrees?

The value of tan 21 degrees can be calculated by constructing an angle of 21° with the x-axis, and then finding the coordinates of the corresponding point (0.9336, 0.3584) on the unit circle. The value of tan 21° is equal to the y-coordinate(0.3584) divided by the x-coordinate (0.9336). ∴ tan 21° = 0.3839

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