Sin 345 Degrees

The value of sin 345 degrees is -0.2588190. . .. Sin 345 degrees in radians is written as sin (345° × π/180°), i.e., sin (23π/12) or sin (6.021385. . .). In this article, we will discuss the methods to find the value of sin 345 degrees with examples.

• Sin 345°: -0.2588190. . .
• Sin 345° in fraction: -(√6 - √2)/4
• Sin (-345 degrees): 0.2588190. . .
• Sin 345° in radians: sin (23π/12) or sin (6.0213859 . . .)

What is the Value of Sin 345 Degrees?

The value of sin 345 degrees in decimal is -0.258819045. . .. Sin 345 degrees can also be expressed using the equivalent of the given angle (345 degrees) in radians (6.02138 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 345 degrees = 345° × (π/180°) rad = 23π/12 or 6.0213 . . .
∴ sin 345° = sin(6.0213) = -(√6 - √2)/4 or -0.2588190. . .

Explanation:

For sin 345 degrees, the angle 345° lies between 270° and 360° (Fourth Quadrant). Since sine function is negative in the fourth quadrant, thus sin 345° value = -(√6 - √2)/4 or -0.2588190. . .
Since the sine function is a periodic function, we can represent sin 345° as, sin 345 degrees = sin(345° + n × 360°), n ∈ Z.
⇒ sin 345° = sin 705° = sin 1065°, and so on.
Note: Since, sine is an odd function, the value of sin(-345°) = -sin(345°).

Methods to Find Value of Sin 345 Degrees

The sine function is negative in the 4th quadrant. The value of sin 345° is given as -0.25881. . .. We can find the value of sin 345 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 345° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 345 degrees as:

• ± √(1-cos²(345°))
• ± tan 345°/√(1 + tan²(345°))
• ± 1/√(1 + cot²(345°))
• ± √(sec²(345°) - 1)/sec 345°
• 1/cosec 345°

Note: Since 345° lies in the 4th Quadrant, the final value of sin 345° will be negative.

We can use trigonometric identities to represent sin 345° as,

• sin(180° - 345°) = sin(-165°)
• -sin(180° + 345°) = -sin 525°
• cos(90° - 345°) = cos(-255°)
• -cos(90° + 345°) = -cos 435°

Sin 345 Degrees Using Unit Circle

To find the value of sin 345 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 345° angle with the positive x-axis.
• The sin of 345 degrees equals the y-coordinate(-0.2588) of the point of intersection (0.9659, -0.2588) of unit circle and r.

Hence the value of sin 345° = y = -0.2588 (approx)

☛ Also Check:

• sin 36 degrees
• sin 3 degrees
• sin 1 degrees
• sin 88 degrees
• sin 220 degrees
• sin 165 degrees

FAQs on Sin 345 Degrees

What is Sin 345 Degrees?

Sin 345 degrees is the value of sine trigonometric function for an angle equal to 345 degrees. The value of sin 345° is -(√6 - √2)/4 or -0.2588 (approx).

How to Find the Value of Sin 345 Degrees?

The value of sin 345 degrees can be calculated by constructing an angle of 345° with the x-axis, and then finding the coordinates of the corresponding point (0.9659, -0.2588) on the unit circle. The value of sin 345° is equal to the y-coordinate (-0.2588). ∴ sin 345° = -0.2588.

How to Find Sin 345° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 345° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(345°))
• ± tan 345°/√(1 + tan²(345°))
• ± 1/√(1 + cot²(345°))
• ± √(sec²(345°) - 1)/sec 345°
• 1/cosec 345°

☛ Also check: trigonometric table

What is the Exact Value of sin 345 Degrees?

The exact value of sin 345 degrees can be given accurately up to 8 decimal places as -0.25881904 and -(√6 - √2)/4 in fraction.

What is the Value of Sin 345 Degrees in Terms of Cot 345°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 345° can be written as -1/√(1 + cot²(345°)). Here, the value of cot 345° is equal to -3.73205.