Sin 356 Degrees

The value of sin 356 degrees is -0.0697564. . .. Sin 356 degrees in radians is written as sin (356° × π/180°), i.e., sin (89π/45) or sin (6.213372. . .). In this article, we will discuss the methods to find the value of sin 356 degrees with examples.

• Sin 356°: -0.0697564. . .
• Sin (-356 degrees): 0.0697564. . .
• Sin 356° in radians: sin (89π/45) or sin (6.2133721 . . .)

What is the Value of Sin 356 Degrees?

The value of sin 356 degrees in decimal is -0.069756473. . .. Sin 356 degrees can also be expressed using the equivalent of the given angle (356 degrees) in radians (6.21337 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 356 degrees = 356° × (π/180°) rad = 89π/45 or 6.2133 . . .
∴ sin 356° = sin(6.2133) = -0.0697564. . .

Explanation:

For sin 356 degrees, the angle 356° lies between 270° and 360° (Fourth Quadrant). Since sine function is negative in the fourth quadrant, thus sin 356° value = -0.0697564. . .
Since the sine function is a periodic function, we can represent sin 356° as, sin 356 degrees = sin(356° + n × 360°), n ∈ Z.
⇒ sin 356° = sin 716° = sin 1076°, and so on.
Note: Since, sine is an odd function, the value of sin(-356°) = -sin(356°).

Methods to Find Value of Sin 356 Degrees

The sine function is negative in the 4th quadrant. The value of sin 356° is given as -0.06975. . .. We can find the value of sin 356 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 356 Degrees Using Unit Circle

To find the value of sin 356 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 356° angle with the positive x-axis.
• The sin of 356 degrees equals the y-coordinate(-0.0698) of the point of intersection (0.9976, -0.0698) of unit circle and r.

Hence the value of sin 356° = y = -0.0698 (approx)

Sin 356° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 356 degrees as:

• ± √(1-cos²(356°))
• ± tan 356°/√(1 + tan²(356°))
• ± 1/√(1 + cot²(356°))
• ± √(sec²(356°) - 1)/sec 356°
• 1/cosec 356°

Note: Since 356° lies in the 4th Quadrant, the final value of sin 356° will be negative.

We can use trigonometric identities to represent sin 356° as,

• sin(180° - 356°) = sin(-176°)
• -sin(180° + 356°) = -sin 536°
• cos(90° - 356°) = cos(-266°)
• -cos(90° + 356°) = -cos 446°

☛ Also Check:

• sin 30 degrees
• sin 360 degrees
• sin 135 degrees
• sin 900 degrees
• sin 66 degrees
• sin 765 degrees

FAQs on Sin 356 Degrees

What is Sin 356 Degrees?

Sin 356 degrees is the value of sine trigonometric function for an angle equal to 356 degrees. The value of sin 356° is -0.0698 (approx).

What is the Exact Value of sin 356 Degrees?

The exact value of sin 356 degrees can be given accurately up to 8 decimal places as -0.06975647.

What is the Value of Sin 356 Degrees in Terms of Tan 356°?

We know, using trig identities, we can write sin 356° as tan 356°/√(1 + tan²(356°)). Here, the value of tan 356° is equal to -0.069926.

How to Find Sin 356° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 356° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(356°))
• ± tan 356°/√(1 + tan²(356°))
• ± 1/√(1 + cot²(356°))
• ± √(sec²(356°) - 1)/sec 356°
• 1/cosec 356°

☛ Also check: trigonometric table

How to Find the Value of Sin 356 Degrees?

The value of sin 356 degrees can be calculated by constructing an angle of 356° with the x-axis, and then finding the coordinates of the corresponding point (0.9976, -0.0698) on the unit circle. The value of sin 356° is equal to the y-coordinate (-0.0698). ∴ sin 356° = -0.0698.