Sin 856 Degrees

The value of sin 856 degrees is 0.6946583. . .. Sin 856 degrees in radians is written as sin (856° × π/180°), i.e., sin (214π/45) or sin (14.940018. . .). In this article, we will discuss the methods to find the value of sin 856 degrees with examples.

• Sin 856°: 0.6946583. . .
• Sin (-856 degrees): -0.6946583. . .
• Sin 856° in radians: sin (214π/45) or sin (14.9400183 . . .)

What is the Value of Sin 856 Degrees?

The value of sin 856 degrees in decimal is 0.694658370. . .. Sin 856 degrees can also be expressed using the equivalent of the given angle (856 degrees) in radians (14.94001 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 856 degrees = 856° × (π/180°) rad = 214π/45 or 14.9400 . . .
∴ sin 856° = sin(14.9400) = 0.6946583. . .

Explanation:

For sin 856°, the angle 856° > 360°. Given the periodic property of the sine function, we can represent it as sin(856° mod 360°) = sin(136°). The angle 856°, coterminal to angle 136°, is located in the Second Quadrant(Quadrant II).
Since sine function is positive in the 2nd quadrant, thus sin 856 degrees value = 0.6946583. . .
Similarly, sin 856° can also be written as, sin 856 degrees = (856° + n × 360°), n ∈ Z.
⇒ sin 856° = sin 1216° = sin 1576°, and so on.
Note: Since, sine is an odd function, the value of sin(-856°) = -sin(856°).

Methods to Find Value of Sin 856 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 856° is given as 0.69465. . .. We can find the value of sin 856 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 856° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 856 degrees as:

• ± √(1-cos²(856°))
• ± tan 856°/√(1 + tan²(856°))
• ± 1/√(1 + cot²(856°))
• ± √(sec²(856°) - 1)/sec 856°
• 1/cosec 856°

Note: Since 856° lies in the 2nd Quadrant, the final value of sin 856° will be positive.

We can use trigonometric identities to represent sin 856° as,

• sin(180° - 856°) = sin(-676°)
• -sin(180° + 856°) = -sin 1036°
• cos(90° - 856°) = cos(-766°)
• -cos(90° + 856°) = -cos 946°

Sin 856 Degrees Using Unit Circle

To find the value of sin 856 degrees using the unit circle, represent 856° in the form (2 × 360°) + 136° [∵ 856°>360°] ∵ sine is a periodic function, sin 856° = sin 136°.

• Rotate ‘r’ anticlockwise to form a 136° or 856° angle with the positive x-axis.
• The sin of 856 degrees equals the y-coordinate(0.6947) of the point of intersection (-0.7193, 0.6947) of unit circle and r.

Hence the value of sin 856° = y = 0.6947 (approx)

☛ Also Check:

• sin 0 degrees
• sin 3 degrees
• sin 1 degrees
• sin 930 degrees
• sin 32 degrees
• sin 78 degrees

FAQs on Sin 856 Degrees

What is Sin 856 Degrees?

Sin 856 degrees is the value of sine trigonometric function for an angle equal to 856 degrees. The value of sin 856° is 0.6947 (approx).

What is the Value of Sin 856° in Terms of Cosec 856°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 856° as 1/cosec(856°). The value of cosec 856° is equal to 1.43955.

How to Find Sin 856° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 856° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(856°))
• ± tan 856°/√(1 + tan²(856°))
• ± 1/√(1 + cot²(856°))
• ± √(sec²(856°) - 1)/sec 856°
• 1/cosec 856°

☛ Also check: trigonometry table

How to Find the Value of Sin 856 Degrees?

The value of sin 856 degrees can be calculated by constructing an angle of 856° with the x-axis, and then finding the coordinates of the corresponding point (-0.7193, 0.6947) on the unit circle. The value of sin 856° is equal to the y-coordinate (0.6947). ∴ sin 856° = 0.6947.

What is the Value of Sin 856 Degrees in Terms of Cos 856°?

Using trigonometric identities, we can write sin 856° in terms of cos 856° as, sin(856°) = √(1-cos²(856°)). Here, the value of cos 856° is equal to -0.7193398.