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Tan 41 Degrees

The value of tan 41 degrees is 0.8692867. . .. Tan 41 degrees in radians is written as tan (41° × π/180°), i.e., tan (0.715584. . .). In this article, we will discuss the methods to find the value of tan 41 degrees with examples.

Tan 41° in decimal: 0.8692867. . .
Tan (-41 degrees): -0.8692867. . .
Tan 41° in radians: tan (0.7155849 . . .)

What is the Value of Tan 41 Degrees?

The value of tan 41 degrees in decimal is 0.869286737. . .. Tan 41 degrees can also be expressed using the equivalent of the given angle (41 degrees) in radians (0.71558 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 41 degrees = 41° × (π/180°) rad = 0.7155 . . .
∴ tan 41° = tan(0.7155) = 0.8692867. . .

Explanation:

For tan 41 degrees, the angle 41° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 41° value = 0.8692867. . .
Since the tangent function is a periodic function, we can represent tan 41° as, tan 41 degrees = tan(41° + n × 180°), n ∈ Z.
⇒ tan 41° = tan 221° = tan 401°, and so on.
Note: Since, tangent is an odd function, the value of tan(-41°) = -tan(41°).

Methods to Find Value of Tan 41 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 41° is given as 0.86928. . .. We can find the value of tan 41 degrees by:

Using Unit Circle
Using Trigonometric Functions

Tan 41 Degrees Using Unit Circle

To find the value of tan 41 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 41° angle with the positive x-axis.
The tan of 41 degrees equals the y-coordinate(0.6561) divided by x-coordinate(0.7547) of the point of intersection (0.7547, 0.6561) of unit circle and r.

Hence the value of tan 41° = y/x = 0.8693 (approx).

Tan 41° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 41 degrees as:

sin(41°)/cos(41°)
± sin 41°/√(1 - sin²(41°))
± √(1 - cos²(41°))/cos 41°
± 1/√(cosec²(41°) - 1)
± √(sec²(41°) - 1)
1/cot 41°

Note: Since 41° lies in the 1st Quadrant, the final value of tan 41° will be positive.

We can use trigonometric identities to represent tan 41° as,

cot(90° - 41°) = cot 49°
-cot(90° + 41°) = -cot 131°
-tan (180° - 41°) = -tan 139°

☛ Also Check:

Examples Using Tan 41 Degrees

Example 1: Find the value of (2 sin (20.5°) cos (20.5°) sec (41°)). [Hint: Use tan 41° = 0.8693]

Solution:

Using sin 2a formula,
2 sin (20.5°) cos (20.5°) = sin (2 × 20.5°) = sin 41°
⇒ 2 sin (20.5°) cos (20.5°) sec(41°) = sin 41° sec 41°
= sin 41°/cos 41° = tan 41°
⇒ (2 sin (20.5°) cos (20.5°) sec(41°)) = 0.8693
Example 2: Using the value of tan 41°, solve: (sec²(41°) - 1).

Solution:
We know, (sec²(41°) - 1) = (tan²(41°)) = 0.7557
⇒ (sec²(41°) - 1) = 0.7557
Example 3: Find the value of 3 tan(41°)/4 tan(139°).

Solution:

Using trigonometric identities, we know, tan(41°) = -tan(180° - 41°) = -tan 139°.
⇒ tan(41°) = -tan(139°)
⇒ Value of 3 tan(41°)/4 tan(139°) = -3/4

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FAQs on Tan 41 Degrees

What is Tan 41 Degrees?

Tan 41 degrees is the value of tangent trigonometric function for an angle equal to 41 degrees. The value of tan 41° is 0.8693 (approx).

What is the Value of Tan 41° in Terms of Cosec 41°?

Since the tangent function can be represented using the cosecant function, we can write tan 41° as 1/√(cosec²(41°) - 1). The value of cosec 41° is equal to 1.52425.

How to Find the Value of Tan 41 Degrees?

The value of tan 41 degrees can be calculated by constructing an angle of 41° with the x-axis, and then finding the coordinates of the corresponding point (0.7547, 0.6561) on the unit circle. The value of tan 41° is equal to the y-coordinate(0.6561) divided by the x-coordinate (0.7547). ∴ tan 41° = 0.8693

What is the Value of Tan 41 Degrees in Terms of Cot 41°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 41° as 1/cot(41°). The value of cot 41° is equal to 1.15036.

How to Find Tan 41° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 41° can be given in terms of other trigonometric functions as:

sin(41°)/cos(41°)
± sin 41°/√(1 - sin²(41°))
± √(1 - cos²(41°))/cos 41°
± 1/√(cosec²(41°) - 1)
± √(sec²(41°) - 1)
1/cot 41°

☛ Also check: trigonometric table

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