Sin 570 Degrees

The value of sin 570 degrees is -0.5. Sin 570 degrees in radians is written as sin (570° × π/180°), i.e., sin (19π/6) or sin (9.948376. . .). In this article, we will discuss the methods to find the value of sin 570 degrees with examples.

• Sin 570°: -0.5
• Sin 570° in fraction: -(1/2)
• Sin (-570 degrees): 0.5
• Sin 570° in radians: sin (19π/6) or sin (9.9483767 . . .)

What is the Value of Sin 570 Degrees?

The value of sin 570 degrees in decimal is -0.5. Sin 570 degrees can also be expressed using the equivalent of the given angle (570 degrees) in radians (9.94837 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 570 degrees = 570° × (π/180°) rad = 19π/6 or 9.9483 . . .
∴ sin 570° = sin(9.9483) = -(1/2) or -0.5

Explanation:

For sin 570°, the angle 570° > 360°. Given the periodic property of the sine function, we can represent it as sin(570° mod 360°) = sin(210°). The angle 570°, coterminal to angle 210°, is located in the Third Quadrant(Quadrant III).
Since sine function is negative in the 3rd quadrant, thus sin 570 degrees value = -(1/2) or -0.5
Similarly, sin 570° can also be written as, sin 570 degrees = (570° + n × 360°), n ∈ Z.
⇒ sin 570° = sin 930° = sin 1290°, and so on.
Note: Since, sine is an odd function, the value of sin(-570°) = -sin(570°).

Methods to Find Value of Sin 570 Degrees

The sine function is negative in the 3rd quadrant. The value of sin 570° is given as -0.5. We can find the value of sin 570 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 570° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 570 degrees as:

• ± √(1-cos²(570°))
• ± tan 570°/√(1 + tan²(570°))
• ± 1/√(1 + cot²(570°))
• ± √(sec²(570°) - 1)/sec 570°
• 1/cosec 570°

Note: Since 570° lies in the 3rd Quadrant, the final value of sin 570° will be negative.

We can use trigonometric identities to represent sin 570° as,

• sin(180° - 570°) = sin(-390°)
• -sin(180° + 570°) = -sin 750°
• cos(90° - 570°) = cos(-480°)
• -cos(90° + 570°) = -cos 660°

Sin 570 Degrees Using Unit Circle

To find the value of sin 570 degrees using the unit circle, represent 570° in the form (1 × 360°) + 210° [∵ 570°>360°] ∵ sine is a periodic function, sin 570° = sin 210°.

• Rotate ‘r’ anticlockwise to form a 210° or 570° angle with the positive x-axis.
• The sin of 570 degrees equals the y-coordinate(-0.5) of the point of intersection (-0.866, -0.5) of unit circle and r.

Hence the value of sin 570° = y = -0.5

☛ Also Check:

• sin 90 degrees
• sin 360 degrees
• sin 11 degrees
• sin 51 degrees
• sin 5 degrees
• sin 39 degrees

FAQs on Sin 570 Degrees

What is Sin 570 Degrees?

Sin 570 degrees is the value of sine trigonometric function for an angle equal to 570 degrees. The value of sin 570° is -(1/2) or -0.5.

What is the Value of Sin 570 Degrees in Terms of Tan 570°?

We know, using trig identities, we can write sin 570° as -tan 570°/√(1 + tan²(570°)). Here, the value of tan 570° is equal to 0.577350.

How to Find Sin 570° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 570° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(570°))
• ± tan 570°/√(1 + tan²(570°))
• ± 1/√(1 + cot²(570°))
• ± √(sec²(570°) - 1)/sec 570°
• 1/cosec 570°

☛ Also check: trigonometric table

What is the Exact Value of sin 570 Degrees?

The exact value of sin 570 degrees is -0.5.

How to Find the Value of Sin 570 Degrees?

The value of sin 570 degrees can be calculated by constructing an angle of 570° with the x-axis, and then finding the coordinates of the corresponding point (-0.866, -0.5) on the unit circle. The value of sin 570° is equal to the y-coordinate (-0.5). ∴ sin 570° = -0.5.