Sin 53 Degrees

The value of sin 53 degrees is 0.7986355. . .. Sin 53 degrees in radians is written as sin (53° × π/180°), i.e., sin (0.925024. . .). In this article, we will discuss the methods to find the value of sin 53 degrees with examples.

• Sin 53°: 0.7986355. . .
• Sin (-53 degrees): -0.7986355. . .
• Sin 53° in radians: sin (0.9250245 . . .)

What is the Value of Sin 53 Degrees?

The value of sin 53 degrees in decimal is 0.798635510. . .. Sin 53 degrees can also be expressed using the equivalent of the given angle (53 degrees) in radians (0.92502 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 53 degrees = 53° × (π/180°) rad = 0.9250 . . .
∴ sin 53° = sin(0.9250) = 0.7986355. . .

Explanation:

For sin 53 degrees, the angle 53° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 53° value = 0.7986355. . .
Since the sine function is a periodic function, we can represent sin 53° as, sin 53 degrees = sin(53° + n × 360°), n ∈ Z.
⇒ sin 53° = sin 413° = sin 773°, and so on.
Note: Since, sine is an odd function, the value of sin(-53°) = -sin(53°).

Methods to Find Value of Sin 53 Degrees

The sine function is positive in the 1st quadrant. The value of sin 53° is given as 0.79863. . .. We can find the value of sin 53 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 53° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 53 degrees as:

• ± √(1-cos²(53°))
• ± tan 53°/√(1 + tan²(53°))
• ± 1/√(1 + cot²(53°))
• ± √(sec²(53°) - 1)/sec 53°
• 1/cosec 53°

Note: Since 53° lies in the 1st Quadrant, the final value of sin 53° will be positive.

We can use trigonometric identities to represent sin 53° as,

• sin(180° - 53°) = sin 127°
• -sin(180° + 53°) = -sin 233°
• cos(90° - 53°) = cos 37°
• -cos(90° + 53°) = -cos 143°

Sin 53 Degrees Using Unit Circle

To find the value of sin 53 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 53° angle with the positive x-axis.
• The sin of 53 degrees equals the y-coordinate(0.7986) of the point of intersection (0.6018, 0.7986) of unit circle and r.

Hence the value of sin 53° = y = 0.7986 (approx)

☛ Also Check:

• sin 120 degrees
• sin 40 degrees
• sin 180 degrees
• sin 780 degrees
• sin 330 degrees
• sin 68 degrees

FAQs on Sin 53 Degrees

What is Sin 53 Degrees?

Sin 53 degrees is the value of sine trigonometric function for an angle equal to 53 degrees. The value of sin 53° is 0.7986 (approx).

What is the Value of Sin 53° in Terms of Sec 53°?

Since the sine function can be represented using the secant function, we can write sin 53° as √(sec²(53°) - 1)/sec 53°. The value of sec 53° is equal to 1.66164.

What is the Value of Sin 53 Degrees in Terms of Cos 53°?

Using trigonometric identities, we can write sin 53° in terms of cos 53° as, sin(53°) = √(1-cos²(53°)). Here, the value of cos 53° is equal to 0.6018150.

How to Find Sin 53° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 53° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(53°))
• ± tan 53°/√(1 + tan²(53°))
• ± 1/√(1 + cot²(53°))
• ± √(sec²(53°) - 1)/sec 53°
• 1/cosec 53°

☛ Also check: trigonometry table

How to Find the Value of Sin 53 Degrees?

The value of sin 53 degrees can be calculated by constructing an angle of 53° with the x-axis, and then finding the coordinates of the corresponding point (0.6018, 0.7986) on the unit circle. The value of sin 53° is equal to the y-coordinate (0.7986). ∴ sin 53° = 0.7986.