Sin 96 Degrees

The value of sin 96 degrees is 0.9945218. . .. Sin 96 degrees in radians is written as sin (96° × π/180°), i.e., sin (8π/15) or sin (1.675516. . .). In this article, we will discuss the methods to find the value of sin 96 degrees with examples.

• Sin 96°: 0.9945218. . .
• Sin (-96 degrees): -0.9945218. . .
• Sin 96° in radians: sin (8π/15) or sin (1.6755160 . . .)

What is the Value of Sin 96 Degrees?

The value of sin 96 degrees in decimal is 0.994521895. . .. Sin 96 degrees can also be expressed using the equivalent of the given angle (96 degrees) in radians (1.67551 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 96 degrees = 96° × (π/180°) rad = 8π/15 or 1.6755 . . .
∴ sin 96° = sin(1.6755) = 0.9945218. . .

Explanation:

For sin 96 degrees, the angle 96° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 96° value = 0.9945218. . .
Since the sine function is a periodic function, we can represent sin 96° as, sin 96 degrees = sin(96° + n × 360°), n ∈ Z.
⇒ sin 96° = sin 456° = sin 816°, and so on.
Note: Since, sine is an odd function, the value of sin(-96°) = -sin(96°).

Methods to Find Value of Sin 96 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 96° is given as 0.99452. . .. We can find the value of sin 96 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 96 Degrees Using Unit Circle

To find the value of sin 96 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 96° angle with the positive x-axis.
• The sin of 96 degrees equals the y-coordinate(0.9945) of the point of intersection (-0.1045, 0.9945) of unit circle and r.

Hence the value of sin 96° = y = 0.9945 (approx)

Sin 96° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 96 degrees as:

• ± √(1-cos²(96°))
• ± tan 96°/√(1 + tan²(96°))
• ± 1/√(1 + cot²(96°))
• ± √(sec²(96°) - 1)/sec 96°
• 1/cosec 96°

Note: Since 96° lies in the 2nd Quadrant, the final value of sin 96° will be positive.

We can use trigonometric identities to represent sin 96° as,

• sin(180° - 96°) = sin 84°
• -sin(180° + 96°) = -sin 276°
• cos(90° - 96°) = cos(-6°)
• -cos(90° + 96°) = -cos 186°

☛ Also Check:

• sin 75 degrees
• sin 90 degrees
• sin 104 degrees
• sin 31 degrees
• sin 78 degrees
• sin 144 degrees

FAQs on Sin 96 Degrees

What is Sin 96 Degrees?

Sin 96 degrees is the value of sine trigonometric function for an angle equal to 96 degrees. The value of sin 96° is 0.9945 (approx).

How to Find Sin 96° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 96° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(96°))
• ± tan 96°/√(1 + tan²(96°))
• ± 1/√(1 + cot²(96°))
• ± √(sec²(96°) - 1)/sec 96°
• 1/cosec 96°

☛ Also check: trigonometry table

What is the Exact Value of sin 96 Degrees?

The exact value of sin 96 degrees can be given accurately up to 8 decimal places as 0.99452189.

How to Find the Value of Sin 96 Degrees?

The value of sin 96 degrees can be calculated by constructing an angle of 96° with the x-axis, and then finding the coordinates of the corresponding point (-0.1045, 0.9945) on the unit circle. The value of sin 96° is equal to the y-coordinate (0.9945). ∴ sin 96° = 0.9945.

What is the Value of Sin 96 Degrees in Terms of Cos 96°?

Using trigonometric identities, we can write sin 96° in terms of cos 96° as, sin(96°) = √(1-cos²(96°)). Here, the value of cos 96° is equal to -0.1045284.