Sin 285 Degrees

The value of sin 285 degrees is -0.9659258. . .. Sin 285 degrees in radians is written as sin (285° × π/180°), i.e., sin (19π/12) or sin (4.974188. . .). In this article, we will discuss the methods to find the value of sin 285 degrees with examples.

• Sin 285°: -0.9659258. . .
• Sin 285° in fraction: -(√6 + √2)/4
• Sin (-285 degrees): 0.9659258. . .
• Sin 285° in radians: sin (19π/12) or sin (4.9741883 . . .)

What is the Value of Sin 285 Degrees?

The value of sin 285 degrees in decimal is -0.965925826. . .. Sin 285 degrees can also be expressed using the equivalent of the given angle (285 degrees) in radians (4.97418 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 285 degrees = 285° × (π/180°) rad = 19π/12 or 4.9741 . . .
∴ sin 285° = sin(4.9741) = -(√6 + √2)/4 or -0.9659258. . .

Explanation:

For sin 285 degrees, the angle 285° lies between 270° and 360° (Fourth Quadrant). Since sine function is negative in the fourth quadrant, thus sin 285° value = -(√6 + √2)/4 or -0.9659258. . .
Since the sine function is a periodic function, we can represent sin 285° as, sin 285 degrees = sin(285° + n × 360°), n ∈ Z.
⇒ sin 285° = sin 645° = sin 1005°, and so on.
Note: Since, sine is an odd function, the value of sin(-285°) = -sin(285°).

Methods to Find Value of Sin 285 Degrees

The sine function is negative in the 4th quadrant. The value of sin 285° is given as -0.96592. . .. We can find the value of sin 285 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 285 Degrees Using Unit Circle

To find the value of sin 285 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 285° angle with the positive x-axis.
• The sin of 285 degrees equals the y-coordinate(-0.9659) of the point of intersection (0.2588, -0.9659) of unit circle and r.

Hence the value of sin 285° = y = -0.9659 (approx)

Sin 285° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 285 degrees as:

• ± √(1-cos²(285°))
• ± tan 285°/√(1 + tan²(285°))
• ± 1/√(1 + cot²(285°))
• ± √(sec²(285°) - 1)/sec 285°
• 1/cosec 285°

Note: Since 285° lies in the 4th Quadrant, the final value of sin 285° will be negative.

We can use trigonometric identities to represent sin 285° as,

• sin(180° - 285°) = sin(-105°)
• -sin(180° + 285°) = -sin 465°
• cos(90° - 285°) = cos(-195°)
• -cos(90° + 285°) = -cos 375°

☛ Also Check:

• sin 75 degrees
• sin 104 degrees
• sin 11 degrees
• sin 240 degrees
• sin 600 degrees
• sin 12 degrees

FAQs on Sin 285 Degrees

What is Sin 285 Degrees?

Sin 285 degrees is the value of sine trigonometric function for an angle equal to 285 degrees. The value of sin 285° is -(√6 + √2)/4 or -0.9659 (approx).

How to Find the Value of Sin 285 Degrees?

The value of sin 285 degrees can be calculated by constructing an angle of 285° with the x-axis, and then finding the coordinates of the corresponding point (0.2588, -0.9659) on the unit circle. The value of sin 285° is equal to the y-coordinate (-0.9659). ∴ sin 285° = -0.9659.

What is the Value of Sin 285 Degrees in Terms of Cos 285°?

Using trigonometric identities, we can write sin 285° in terms of cos 285° as, sin(285°) = -√(1-cos²(285°)). Here, the value of cos 285° is equal to (√6-√2)/4.

What is the Exact Value of sin 285 Degrees?

The exact value of sin 285 degrees can be given accurately up to 8 decimal places as -0.96592582 and -(√6 + √2)/4 in fraction.

How to Find Sin 285° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 285° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(285°))
• ± tan 285°/√(1 + tan²(285°))
• ± 1/√(1 + cot²(285°))
• ± √(sec²(285°) - 1)/sec 285°
• 1/cosec 285°

☛ Also check: trigonometry table