Sin 66 Degrees

The value of sin 66 degrees is 0.9135454. . .. Sin 66 degrees in radians is written as sin (66° × π/180°), i.e., sin (11π/30) or sin (1.151917. . .). In this article, we will discuss the methods to find the value of sin 66 degrees with examples.

• Sin 66°: 0.9135454. . .
• Sin (-66 degrees): -0.9135454. . .
• Sin 66° in radians: sin (11π/30) or sin (1.1519173 . . .)

What is the Value of Sin 66 Degrees?

The value of sin 66 degrees in decimal is 0.913545457. . .. Sin 66 degrees can also be expressed using the equivalent of the given angle (66 degrees) in radians (1.15191 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 66 degrees = 66° × (π/180°) rad = 11π/30 or 1.1519 . . .
∴ sin 66° = sin(1.1519) = 0.9135454. . .

Explanation:

For sin 66 degrees, the angle 66° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 66° value = 0.9135454. . .
Since the sine function is a periodic function, we can represent sin 66° as, sin 66 degrees = sin(66° + n × 360°), n ∈ Z.
⇒ sin 66° = sin 426° = sin 786°, and so on.
Note: Since, sine is an odd function, the value of sin(-66°) = -sin(66°).

Methods to Find Value of Sin 66 Degrees

The sine function is positive in the 1st quadrant. The value of sin 66° is given as 0.91354. . .. We can find the value of sin 66 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 66° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 66 degrees as:

• ± √(1-cos²(66°))
• ± tan 66°/√(1 + tan²(66°))
• ± 1/√(1 + cot²(66°))
• ± √(sec²(66°) - 1)/sec 66°
• 1/cosec 66°

Note: Since 66° lies in the 1st Quadrant, the final value of sin 66° will be positive.

We can use trigonometric identities to represent sin 66° as,

• sin(180° - 66°) = sin 114°
• -sin(180° + 66°) = -sin 246°
• cos(90° - 66°) = cos 24°
• -cos(90° + 66°) = -cos 156°

Sin 66 Degrees Using Unit Circle

To find the value of sin 66 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 66° angle with the positive x-axis.
• The sin of 66 degrees equals the y-coordinate(0.9135) of the point of intersection (0.4067, 0.9135) of unit circle and r.

Hence the value of sin 66° = y = 0.9135 (approx)

☛ Also Check:

• sin 360 degrees
• sin 135 degrees
• sin 11 degrees
• sin 27 degrees
• sin 38 degrees
• sin 71 degrees

FAQs on Sin 66 Degrees

What is Sin 66 Degrees?

Sin 66 degrees is the value of sine trigonometric function for an angle equal to 66 degrees. The value of sin 66° is 0.9135 (approx).

What is the Exact Value of sin 66 Degrees?

The exact value of sin 66 degrees can be given accurately up to 8 decimal places as 0.91354545.

How to Find the Value of Sin 66 Degrees?

The value of sin 66 degrees can be calculated by constructing an angle of 66° with the x-axis, and then finding the coordinates of the corresponding point (0.4067, 0.9135) on the unit circle. The value of sin 66° is equal to the y-coordinate (0.9135). ∴ sin 66° = 0.9135.

How to Find Sin 66° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 66° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(66°))
• ± tan 66°/√(1 + tan²(66°))
• ± 1/√(1 + cot²(66°))
• ± √(sec²(66°) - 1)/sec 66°
• 1/cosec 66°

☛ Also check: trigonometric table

What is the Value of Sin 66 Degrees in Terms of Tan 66°?

We know, using trig identities, we can write sin 66° as tan 66°/√(1 + tan²(66°)). Here, the value of tan 66° is equal to 2.246036.