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Tan 20 Degrees

The value of tan 20 degrees is 0.3639702. . .. Tan 20 degrees in radians is written as tan (20° × π/180°), i.e., tan (π/9) or tan (0.349065. . .). In this article, we will discuss the methods to find the value of tan 20 degrees with examples.

Tan 20° in decimal: 0.3639702. . .
Tan (-20 degrees): -0.3639702. . .
Tan 20° in radians: tan (π/9) or tan (0.3490658 . . .)

What is the Value of Tan 20 Degrees?

The value of tan 20 degrees in decimal is 0.363970234. . .. Tan 20 degrees can also be expressed using the equivalent of the given angle (20 degrees) in radians (0.34906 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 20 degrees = 20° × (π/180°) rad = π/9 or 0.3490 . . .
∴ tan 20° = tan(0.3490) = 0.3639702. . .

Explanation:

For tan 20 degrees, the angle 20° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 20° value = 0.3639702. . .
Since the tangent function is a periodic function, we can represent tan 20° as, tan 20 degrees = tan(20° + n × 180°), n ∈ Z.
⇒ tan 20° = tan 200° = tan 380°, and so on.
Note: Since, tangent is an odd function, the value of tan(-20°) = -tan(20°).

Methods to Find Value of Tan 20 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 20° is given as 0.36397. . .. We can find the value of tan 20 degrees by:

Using Unit Circle
Using Trigonometric Functions

Tan 20 Degrees Using Unit Circle

To find the value of tan 20 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 20° angle with the positive x-axis.
The tan of 20 degrees equals the y-coordinate(0.342) divided by x-coordinate(0.9397) of the point of intersection (0.9397, 0.342) of unit circle and r.

Hence the value of tan 20° = y/x = 0.364 (approx).

Tan 20° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 20 degrees as:

sin(20°)/cos(20°)
± sin 20°/√(1 - sin²(20°))
± √(1 - cos²(20°))/cos 20°
± 1/√(cosec²(20°) - 1)
± √(sec²(20°) - 1)
1/cot 20°

Note: Since 20° lies in the 1st Quadrant, the final value of tan 20° will be positive.

We can use trigonometric identities to represent tan 20° as,

cot(90° - 20°) = cot 70°
-cot(90° + 20°) = -cot 110°
-tan (180° - 20°) = -tan 160°

☛ Also Check:

Examples Using Tan 20 Degrees

Example 1: Find the value of (2 sin (10°) cos (10°) sec (20°)). [Hint: Use tan 20° = 0.364]

Solution:

Using sin 2a formula,
2 sin (10°) cos (10°) = sin (2 × 10°) = sin 20°
⇒ 2 sin (10°) cos (10°) sec(20°) = sin 20° sec 20°
= sin 20°/cos 20° = tan 20°
⇒ (2 sin (10°) cos (10°) sec(20°)) = 0.364
Example 2: Find the value of 2 tan(20°)/10 tan(160°).

Solution:

Using trigonometric identities, we know, tan(20°) = -tan(180° - 20°) = -tan 160°.
⇒ tan(20°) = -tan(160°)
⇒ Value of 2 tan(20°)/10 tan(160°) = -2/10 = -1/5
Example 3: Using the value of tan 20°, solve: (sec²(20°) - 1).

Solution:
We know, (sec²(20°) - 1) = (tan²(20°)) = 0.1325
⇒ (sec²(20°) - 1) = 0.1325

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FAQs on Tan 20 Degrees

What is Tan 20 Degrees?

Tan 20 degrees is the value of tangent trigonometric function for an angle equal to 20 degrees. The value of tan 20° is 0.364 (approx).

What is the Value of Tan 20 Degrees in Terms of Sin 20°?

Using trigonometric identities, we can write tan 20° in terms of sin 20° as, tan(20°) = sin 20°/√(1 - sin²(20°)) . Here, the value of sin 20° is equal to 0.342.

How to Find Tan 20° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 20° can be given in terms of other trigonometric functions as:

sin(20°)/cos(20°)
± sin 20°/√(1 - sin²(20°))
± √(1 - cos²(20°))/cos 20°
± 1/√(cosec²(20°) - 1)
± √(sec²(20°) - 1)
1/cot 20°

☛ Also check: trigonometric table

How to Find the Value of Tan 20 Degrees?

The value of tan 20 degrees can be calculated by constructing an angle of 20° with the x-axis, and then finding the coordinates of the corresponding point (0.9397, 0.342) on the unit circle. The value of tan 20° is equal to the y-coordinate(0.342) divided by the x-coordinate (0.9397). ∴ tan 20° = 0.364

What is the Exact Value of tan 20 Degrees?

The exact value of tan 20 degrees can be given accurately up to 8 decimal places as 0.36397023.

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