Sin 57 Degrees

The value of sin 57 degrees is 0.8386705. . .. Sin 57 degrees in radians is written as sin (57° × π/180°), i.e., sin (19π/60) or sin (0.994837. . .). In this article, we will discuss the methods to find the value of sin 57 degrees with examples.

• Sin 57°: 0.8386705. . .
• Sin (-57 degrees): -0.8386705. . .
• Sin 57° in radians: sin (19π/60) or sin (0.9948376 . . .)

What is the Value of Sin 57 Degrees?

The value of sin 57 degrees in decimal is 0.838670567. . .. Sin 57 degrees can also be expressed using the equivalent of the given angle (57 degrees) in radians (0.99483 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 57 degrees = 57° × (π/180°) rad = 19π/60 or 0.9948 . . .
∴ sin 57° = sin(0.9948) = 0.8386705. . .

Explanation:

For sin 57 degrees, the angle 57° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 57° value = 0.8386705. . .
Since the sine function is a periodic function, we can represent sin 57° as, sin 57 degrees = sin(57° + n × 360°), n ∈ Z.
⇒ sin 57° = sin 417° = sin 777°, and so on.
Note: Since, sine is an odd function, the value of sin(-57°) = -sin(57°).

Methods to Find Value of Sin 57 Degrees

The sine function is positive in the 1st quadrant. The value of sin 57° is given as 0.83867. . .. We can find the value of sin 57 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 57° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 57 degrees as:

• ± √(1-cos²(57°))
• ± tan 57°/√(1 + tan²(57°))
• ± 1/√(1 + cot²(57°))
• ± √(sec²(57°) - 1)/sec 57°
• 1/cosec 57°

Note: Since 57° lies in the 1st Quadrant, the final value of sin 57° will be positive.

We can use trigonometric identities to represent sin 57° as,

• sin(180° - 57°) = sin 123°
• -sin(180° + 57°) = -sin 237°
• cos(90° - 57°) = cos 33°
• -cos(90° + 57°) = -cos 147°

Sin 57 Degrees Using Unit Circle

To find the value of sin 57 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 57° angle with the positive x-axis.
• The sin of 57 degrees equals the y-coordinate(0.8387) of the point of intersection (0.5446, 0.8387) of unit circle and r.

Hence the value of sin 57° = y = 0.8387 (approx)

☛ Also Check:

• sin 10 degrees
• sin 0 degrees
• sin 40 degrees
• sin 46 degrees
• sin 27 degrees
• sin 125 degrees

FAQs on Sin 57 Degrees

What is Sin 57 Degrees?

Sin 57 degrees is the value of sine trigonometric function for an angle equal to 57 degrees. The value of sin 57° is 0.8387 (approx).

What is the Value of Sin 57° in Terms of Sec 57°?

Since the sine function can be represented using the secant function, we can write sin 57° as √(sec²(57°) - 1)/sec 57°. The value of sec 57° is equal to 1.836078.

What is the Value of Sin 57 Degrees in Terms of Tan 57°?

We know, using trig identities, we can write sin 57° as tan 57°/√(1 + tan²(57°)). Here, the value of tan 57° is equal to 1.539864.

How to Find Sin 57° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 57° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(57°))
• ± tan 57°/√(1 + tan²(57°))
• ± 1/√(1 + cot²(57°))
• ± √(sec²(57°) - 1)/sec 57°
• 1/cosec 57°

☛ Also check: trigonometric table

How to Find the Value of Sin 57 Degrees?

The value of sin 57 degrees can be calculated by constructing an angle of 57° with the x-axis, and then finding the coordinates of the corresponding point (0.5446, 0.8387) on the unit circle. The value of sin 57° is equal to the y-coordinate (0.8387). ∴ sin 57° = 0.8387.