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Sin 300 Degrees

The value of sin 300 degrees is -0.8660254. . .. Sin 300 degrees in radians is written as sin (300° × π/180°), i.e., sin (5π/3) or sin (5.235987. . .). In this article, we will discuss the methods to find the value of sin 300 degrees with examples.

Sin 300°: -0.8660254. . .
Sin 300° in fraction: -(√3/2)
Sin (-300 degrees): 0.8660254. . .
Sin 300° in radians: sin (5π/3) or sin (5.2359877 . . .)

What is the Value of Sin 300 Degrees?

The value of sin 300 degrees in decimal is -0.866025403. . .. Sin 300 degrees can also be expressed using the equivalent of the given angle (300 degrees) in radians (5.23598 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 300 degrees = 300° × (π/180°) rad = 5π/3 or 5.2359 . . .
∴ sin 300° = sin(5.2359) = -(√3/2) or -0.8660254. . .

Explanation:

For sin 300 degrees, the angle 300° lies between 270° and 360° (Fourth Quadrant). Since sine function is negative in the fourth quadrant, thus sin 300° value = -(√3/2) or -0.8660254. . .
Since the sine function is a periodic function, we can represent sin 300° as, sin 300 degrees = sin(300° + n × 360°), n ∈ Z.
⇒ sin 300° = sin 660° = sin 1020°, and so on.
Note: Since, sine is an odd function, the value of sin(-300°) = -sin(300°).

Methods to Find Value of Sin 300 Degrees

The sine function is negative in the 4th quadrant. The value of sin 300° is given as -0.86602. . .. We can find the value of sin 300 degrees by:

Using Trigonometric Functions
Using Unit Circle

Sin 300° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 300 degrees as:

± √(1-cos²(300°))
± tan 300°/√(1 + tan²(300°))
± 1/√(1 + cot²(300°))
± √(sec²(300°) - 1)/sec 300°
1/cosec 300°

Note: Since 300° lies in the 4th Quadrant, the final value of sin 300° will be negative.

We can use trigonometric identities to represent sin 300° as,

sin(180° - 300°) = sin(-120°)
-sin(180° + 300°) = -sin 480°
cos(90° - 300°) = cos(-210°)
-cos(90° + 300°) = -cos 390°

Sin 300 Degrees Using Unit Circle

To find the value of sin 300 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form a 300° angle with the positive x-axis.
The sin of 300 degrees equals the y-coordinate(-0.866) of the point of intersection (0.5, -0.866) of unit circle and r.

Hence the value of sin 300° = y = -0.866 (approx)

☛ Also Check:

Examples Using Sin 300 Degrees

Example 1: Simplify: 2 (sin 300°/sin 660°)

Solution:

We know sin 300° = sin 660°
⇒ 2 sin 300°/sin 660° = 2(sin 300°/sin 300°)
= 2(1) = 2
Example 2: Using the value of sin 300°, solve: (1-cos²(300°)).

Solution:
We know, (1-cos²(300°)) = (sin²(300°)) = 0.75
⇒ (1-cos²(300°)) = 0.75
Example 3: Find the value of 2 × (sin 150° cos 150°). [Hint: Use sin 300° = -0.866]

Solution:

Using the sin 2a formula,
2 sin 150° cos 150° = sin(2 × 150°) = sin 300°
∵ sin 300° = -0.866
⇒ 2 × (sin 150° cos 150°) = -0.866

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FAQs on Sin 300 Degrees

What is Sin 300 Degrees?

Sin 300 degrees is the value of sine trigonometric function for an angle equal to 300 degrees. The value of sin 300° is -(√3/2) or -0.866 (approx).

How to Find the Value of Sin 300 Degrees?

The value of sin 300 degrees can be calculated by constructing an angle of 300° with the x-axis, and then finding the coordinates of the corresponding point (0.5, -0.866) on the unit circle. The value of sin 300° is equal to the y-coordinate (-0.866). ∴ sin 300° = -0.866.

What is the Value of Sin 300° in Terms of Sec 300°?

Since the sine function can be represented using the secant function, we can write sin 300° as -√(sec²(300°) - 1)/sec 300°. The value of sec 300° is equal to 2.

What is the Value of Sin 300 Degrees in Terms of Cot 300°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 300° can be written as -1/√(1 + cot²(300°)). Here, the value of cot 300° is equal to -0.57735.

How to Find Sin 300° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 300° can be given in terms of other trigonometric functions as:

± √(1-cos²(300°))
± tan 300°/√(1 + tan²(300°))
± 1/√(1 + cot²(300°))
± √(sec²(300°) - 1)/sec 300°
1/cosec 300°

☛ Also check: trigonometric table

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