Cos 41 Degrees

The value of cos 41 degrees is 0.7547095. . .. Cos 41 degrees in radians is written as cos (41° × π/180°), i.e., cos (0.715584. . .). In this article, we will discuss the methods to find the value of cos 41 degrees with examples.

• Cos 41°: 0.7547095. . .
• Cos (-41 degrees): 0.7547095. . .
• Cos 41° in radians: cos (0.7155849 . . .)

What is the Value of Cos 41 Degrees?

The value of cos 41 degrees in decimal is 0.754709580. . .. Cos 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 . . .
∴ cos 41° = cos(0.7155) = 0.7547095. . .

Explanation:

For cos 41 degrees, the angle 41° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 41° value = 0.7547095. . .
Since the cosine function is a periodic function, we can represent cos 41° as, cos 41 degrees = cos(41° + n × 360°), n ∈ Z.
⇒ cos 41° = cos 401° = cos 761°, and so on.
Note: Since, cosine is an even function, the value of cos(-41°) = cos(41°).

Methods to Find Value of Cos 41 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 41° is given as 0.75470. . .. We can find the value of cos 41 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 41 Degrees Using Unit Circle

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

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

Hence the value of cos 41° = x = 0.7547 (approx)

Cos 41° in Terms of Trigonometric Functions

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

• ± √(1-sin²(41°))
• ± 1/√(1 + tan²(41°))
• ± cot 41°/√(1 + cot²(41°))
• ±√(cosec²(41°) - 1)/cosec 41°
• 1/sec 41°

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

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

• -cos(180° - 41°) = -cos 139°
• -cos(180° + 41°) = -cos 221°
• sin(90° + 41°) = sin 131°
• sin(90° - 41°) = sin 49°

☛ Also Check:

• cos 210 degrees
• cos 18 degrees
• cos 1 degrees
• cos 50 degrees
• cos 126 degrees
• cos 51 degrees

FAQs on Cos 41 Degrees

What is Cos 41 Degrees?

Cos 41 degrees is the value of cosine trigonometric function for an angle equal to 41 degrees. The value of cos 41° is 0.7547 (approx)

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

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

• ± √(1-sin²(41°))
• ± 1/√(1 + tan²(41°))
• ± cot 41°/√(1 + cot²(41°))
• ± √(cosec²(41°) - 1)/cosec 41°
• 1/sec 41°

☛ Also check: trigonometric table

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

We know, using trig identities, we can write cos 41° as 1/√(1 + tan²(41°)). Here, the value of tan 41° is equal to 0.869286.

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

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

How to Find the Value of Cos 41 Degrees?

The value of cos 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 cos 41° is equal to the x-coordinate (0.7547). ∴ cos 41° = 0.7547.