Sin 49 Degrees

The value of sin 49 degrees is 0.7547095. . .. Sin 49 degrees in radians is written as sin (49° × π/180°), i.e., sin (0.855211. . .). In this article, we will discuss the methods to find the value of sin 49 degrees with examples.

• Sin 49°: 0.7547095. . .
• Sin (-49 degrees): -0.7547095. . .
• Sin 49° in radians: sin (0.8552113 . . .)

What is the Value of Sin 49 Degrees?

The value of sin 49 degrees in decimal is 0.754709580. . .. Sin 49 degrees can also be expressed using the equivalent of the given angle (49 degrees) in radians (0.85521 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 49 degrees = 49° × (π/180°) rad = 0.8552 . . .
∴ sin 49° = sin(0.8552) = 0.7547095. . .

Explanation:

For sin 49 degrees, the angle 49° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 49° value = 0.7547095. . .
Since the sine function is a periodic function, we can represent sin 49° as, sin 49 degrees = sin(49° + n × 360°), n ∈ Z.
⇒ sin 49° = sin 409° = sin 769°, and so on.
Note: Since, sine is an odd function, the value of sin(-49°) = -sin(49°).

Methods to Find Value of Sin 49 Degrees

The sine function is positive in the 1st quadrant. The value of sin 49° is given as 0.75470. . .. We can find the value of sin 49 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 49 Degrees Using Unit Circle

To find the value of sin 49 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 49° angle with the positive x-axis.
• The sin of 49 degrees equals the y-coordinate(0.7547) of the point of intersection (0.6561, 0.7547) of unit circle and r.

Hence the value of sin 49° = y = 0.7547 (approx)

Sin 49° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 49 degrees as:

• ± √(1-cos²(49°))
• ± tan 49°/√(1 + tan²(49°))
• ± 1/√(1 + cot²(49°))
• ± √(sec²(49°) - 1)/sec 49°
• 1/cosec 49°

Note: Since 49° lies in the 1st Quadrant, the final value of sin 49° will be positive.

We can use trigonometric identities to represent sin 49° as,

• sin(180° - 49°) = sin 131°
• -sin(180° + 49°) = -sin 229°
• cos(90° - 49°) = cos 41°
• -cos(90° + 49°) = -cos 139°

☛ Also Check:

• sin 30 degrees
• sin 11 degrees
• sin 104 degrees
• sin 79 degrees
• sin 585 degrees
• sin 19 degrees

FAQs on Sin 49 Degrees

What is Sin 49 Degrees?

Sin 49 degrees is the value of sine trigonometric function for an angle equal to 49 degrees. The value of sin 49° is 0.7547 (approx).

How to Find Sin 49° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 49° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(49°))
• ± tan 49°/√(1 + tan²(49°))
• ± 1/√(1 + cot²(49°))
• ± √(sec²(49°) - 1)/sec 49°
• 1/cosec 49°

☛ Also check: trigonometric table

How to Find the Value of Sin 49 Degrees?

The value of sin 49 degrees can be calculated by constructing an angle of 49° with the x-axis, and then finding the coordinates of the corresponding point (0.6561, 0.7547) on the unit circle. The value of sin 49° is equal to the y-coordinate (0.7547). ∴ sin 49° = 0.7547.

What is the Value of Sin 49 Degrees in Terms of Cos 49°?

Using trigonometric identities, we can write sin 49° in terms of cos 49° as, sin(49°) = √(1-cos²(49°)). Here, the value of cos 49° is equal to 0.6560590.

What is the Value of Sin 49° in Terms of Sec 49°?

Since the sine function can be represented using the secant function, we can write sin 49° as √(sec²(49°) - 1)/sec 49°. The value of sec 49° is equal to 1.524253.