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Tan 1 Degrees

The value of tan 1 degrees is 0.0174550. . .. Tan 1 degrees in radians is written as tan (1° × π/180°), i.e., tan (0.017453. . .). In this article, we will discuss the methods to find the value of tan 1 degrees with examples.

Tan 1° in decimal: 0.0174550. . .
Tan (-1 degrees): -0.0174550. . .
Tan 1° in radians: tan (0.0174532 . . .)

What is the Value of Tan 1 Degrees?

The value of tan 1 degrees in decimal is 0.017455064. . .. Tan 1 degrees can also be expressed using the equivalent of the given angle (1 degrees) in radians (0.01745 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1 degrees = 1° × (π/180°) rad = 0.0174 . . .
∴ tan 1° = tan(0.0174) = 0.0174550. . .

Explanation:

For tan 1 degrees, the angle 1° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 1° value = 0.0174550. . .
Since the tangent function is a periodic function, we can represent tan 1° as, tan 1 degrees = tan(1° + n × 180°), n ∈ Z.
⇒ tan 1° = tan 181° = tan 361°, and so on.
Note: Since, tangent is an odd function, the value of tan(-1°) = -tan(1°).

Methods to Find Value of Tan 1 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 1° is given as 0.01745. . .. We can find the value of tan 1 degrees by:

Using Unit Circle
Using Trigonometric Functions

Tan 1 Degrees Using Unit Circle

To find the value of tan 1 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 1° angle with the positive x-axis.
The tan of 1 degrees equals the y-coordinate(0.0175) divided by x-coordinate(0.9998) of the point of intersection (0.9998, 0.0175) of unit circle and r.

Hence the value of tan 1° = y/x = 0.0175 (approx).

Tan 1° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 1 degrees as:

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

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

We can use trigonometric identities to represent tan 1° as,

cot(90° - 1°) = cot 89°
-cot(90° + 1°) = -cot 91°
-tan (180° - 1°) = -tan 179°

☛ Also Check:

Examples Using Tan 1 Degrees

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

Solution:
We know, (sec²(1°) - 1) = (tan²(1°)) = 0.0003
⇒ (sec²(1°) - 1) = 0.0003
Example 2: Simplify: 8 (tan 1°/cot 89°)

Solution:

We know tan 1° = cot 89°
⇒ 8 tan 1°/cot 89° = 8 (tan 1°/tan 1°)
= 8(1) = 8
Example 3: Find the value of 5 tan(1°)/10 tan(179°).

Solution:

Using trigonometric identities, we know, tan(1°) = -tan(180° - 1°) = -tan 179°.
⇒ tan(1°) = -tan(179°)
⇒ Value of 5 tan(1°)/10 tan(179°) = -5/10 = -1/2

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FAQs on Tan 1 Degrees

What is Tan 1 Degrees?

Tan 1 degrees is the value of tangent trigonometric function for an angle equal to 1 degrees. The value of tan 1° is 0.0175 (approx).

What is the Exact Value of tan 1 Degrees?

The exact value of tan 1 degrees can be given accurately up to 8 decimal places as 0.01745506.

How to Find the Value of Tan 1 Degrees?

The value of tan 1 degrees can be calculated by constructing an angle of 1° with the x-axis, and then finding the coordinates of the corresponding point (0.9998, 0.0175) on the unit circle. The value of tan 1° is equal to the y-coordinate(0.0175) divided by the x-coordinate (0.9998). ∴ tan 1° = 0.0175

What is the Value of Tan 1 Degrees in Terms of Sin 1°?

Using trigonometric identities, we can write tan 1° in terms of sin 1° as, tan(1°) = sin 1°/√(1 - sin²(1°)) . Here, the value of sin 1° is equal to 0.0175.

How to Find Tan 1° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 1° can be given in terms of other trigonometric functions as:

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

☛ Also check: trigonometric table

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