# Tan 20 Tan 40 Tan 80

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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°).

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## 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:

• tan 15 degrees
• tan 20 degrees
• tan 180 degrees
• tan 76 degrees
• tan 1050 degrees
• tan 900 degrees

## 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.

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### 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.

### Tan 20 Tan 40 Tan 80

Sumber: https://www.cuemath.com/trigonometry/tan-20-degrees/

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