Sin 41 Degrees

The value of sin 41 degrees is 0.6560590. . .. Sin 41 degrees in radians is written as sin (41° × π/180°), i.e., sin (0.715584. . .). In this article, we will discuss the methods to find the value of sin 41 degrees with examples.

• Sin 41°: 0.6560590. . .
• Sin (-41 degrees): -0.6560590. . .
• Sin 41° in radians: sin (0.7155849 . . .)

What is the Value of Sin 41 Degrees?

The value of sin 41 degrees in decimal is 0.656059028. . .. Sin 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 . . .
∴ sin 41° = sin(0.7155) = 0.6560590. . .

Explanation:

For sin 41 degrees, the angle 41° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 41° value = 0.6560590. . .
Since the sine function is a periodic function, we can represent sin 41° as, sin 41 degrees = sin(41° + n × 360°), n ∈ Z.
⇒ sin 41° = sin 401° = sin 761°, and so on.
Note: Since, sine is an odd function, the value of sin(-41°) = -sin(41°).

Methods to Find Value of Sin 41 Degrees

The sine function is positive in the 1st quadrant. The value of sin 41° is given as 0.65605. . .. We can find the value of sin 41 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 41° in Terms of Trigonometric Functions

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

• ± √(1-cos²(41°))
• ± tan 41°/√(1 + tan²(41°))
• ± 1/√(1 + cot²(41°))
• ± √(sec²(41°) - 1)/sec 41°
• 1/cosec 41°

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

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

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

Sin 41 Degrees Using Unit Circle

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

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

Hence the value of sin 41° = y = 0.6561 (approx)

☛ Also Check:

• sin 53 degrees
• sin 10 degrees
• sin 3 degrees
• sin 69 degrees
• sin 54 degrees
• sin 16 degrees

FAQs on Sin 41 Degrees

What is Sin 41 Degrees?

Sin 41 degrees is the value of sine trigonometric function for an angle equal to 41 degrees. The value of sin 41° is 0.6561 (approx).

How to Find the Value of Sin 41 Degrees?

The value of sin 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 sin 41° is equal to the y-coordinate (0.6561). ∴ sin 41° = 0.6561.

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

We can represent the sine function in terms of the cotangent function using trig identities, sin 41° can be written as 1/√(1 + cot²(41°)). Here, the value of cot 41° is equal to 1.15036.

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

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

• ± √(1-cos²(41°))
• ± tan 41°/√(1 + tan²(41°))
• ± 1/√(1 + cot²(41°))
• ± √(sec²(41°) - 1)/sec 41°
• 1/cosec 41°

☛ Also check: trigonometric table

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

Since the cosecant function is the reciprocal of the sine function, we can write sin 41° as 1/cosec(41°). The value of cosec 41° is equal to 1.52425.