Sin 39 Degrees

The value of sin 39 degrees is 0.6293203. . .. Sin 39 degrees in radians is written as sin (39° × π/180°), i.e., sin (13π/60) or sin (0.680678. . .). In this article, we will discuss the methods to find the value of sin 39 degrees with examples.

• Sin 39°: 0.6293203. . .
• Sin (-39 degrees): -0.6293203. . .
• Sin 39° in radians: sin (13π/60) or sin (0.6806784 . . .)

What is the Value of Sin 39 Degrees?

The value of sin 39 degrees in decimal is 0.629320391. . .. Sin 39 degrees can also be expressed using the equivalent of the given angle (39 degrees) in radians (0.68067 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 39 degrees = 39° × (π/180°) rad = 13π/60 or 0.6806 . . .
∴ sin 39° = sin(0.6806) = 0.6293203. . .

Explanation:

For sin 39 degrees, the angle 39° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 39° value = 0.6293203. . .
Since the sine function is a periodic function, we can represent sin 39° as, sin 39 degrees = sin(39° + n × 360°), n ∈ Z.
⇒ sin 39° = sin 399° = sin 759°, and so on.
Note: Since, sine is an odd function, the value of sin(-39°) = -sin(39°).

Methods to Find Value of Sin 39 Degrees

The sine function is positive in the 1st quadrant. The value of sin 39° is given as 0.62932. . .. We can find the value of sin 39 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 39 Degrees Using Unit Circle

To find the value of sin 39 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 39° angle with the positive x-axis.
• The sin of 39 degrees equals the y-coordinate(0.6293) of the point of intersection (0.7771, 0.6293) of unit circle and r.

Hence the value of sin 39° = y = 0.6293 (approx)

Sin 39° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 39 degrees as:

• ± √(1-cos²(39°))
• ± tan 39°/√(1 + tan²(39°))
• ± 1/√(1 + cot²(39°))
• ± √(sec²(39°) - 1)/sec 39°
• 1/cosec 39°

Note: Since 39° lies in the 1st Quadrant, the final value of sin 39° will be positive.

We can use trigonometric identities to represent sin 39° as,

• sin(180° - 39°) = sin 141°
• -sin(180° + 39°) = -sin 219°
• cos(90° - 39°) = cos 51°
• -cos(90° + 39°) = -cos 129°

☛ Also Check:

• sin 20 degrees
• sin 180 degrees
• sin 1 degrees
• sin 225 degrees
• sin 170 degrees
• sin 165 degrees

FAQs on Sin 39 Degrees

What is Sin 39 Degrees?

Sin 39 degrees is the value of sine trigonometric function for an angle equal to 39 degrees. The value of sin 39° is 0.6293 (approx).

What is the Exact Value of sin 39 Degrees?

The exact value of sin 39 degrees can be given accurately up to 8 decimal places as 0.62932039.

How to Find Sin 39° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 39° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(39°))
• ± tan 39°/√(1 + tan²(39°))
• ± 1/√(1 + cot²(39°))
• ± √(sec²(39°) - 1)/sec 39°
• 1/cosec 39°

☛ Also check: trigonometry table

What is the Value of Sin 39 Degrees in Terms of Tan 39°?

We know, using trig identities, we can write sin 39° as tan 39°/√(1 + tan²(39°)). Here, the value of tan 39° is equal to 0.809784.

How to Find the Value of Sin 39 Degrees?

The value of sin 39 degrees can be calculated by constructing an angle of 39° with the x-axis, and then finding the coordinates of the corresponding point (0.7771, 0.6293) on the unit circle. The value of sin 39° is equal to the y-coordinate (0.6293). ∴ sin 39° = 0.6293.