Sin 390 Degrees

The value of sin 390 degrees is 0.5. Sin 390 degrees in radians is written as sin (390° × π/180°), i.e., sin (13π/6) or sin (6.806784. . .). In this article, we will discuss the methods to find the value of sin 390 degrees with examples.

• Sin 390°: 0.5
• Sin 390° in fraction: 1/2
• Sin (-390 degrees): -0.5
• Sin 390° in radians: sin (13π/6) or sin (6.8067840 . . .)

What is the Value of Sin 390 Degrees?

The value of sin 390 degrees in decimal is 0.5. Sin 390 degrees can also be expressed using the equivalent of the given angle (390 degrees) in radians (6.80678 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 390 degrees = 390° × (π/180°) rad = 13π/6 or 6.8067 . . .
∴ sin 390° = sin(6.8067) = 1/2 or 0.5

Explanation:

For sin 390°, the angle 390° > 360°. Given the periodic property of the sine function, we can represent it as sin(390° mod 360°) = sin(30°). The angle 390°, coterminal to angle 30°, is located in the First Quadrant(Quadrant I).
Since sine function is positive in the 1st quadrant, thus sin 390 degrees value = 1/2 or 0.5
Similarly, sin 390° can also be written as, sin 390 degrees = (390° + n × 360°), n ∈ Z.
⇒ sin 390° = sin 750° = sin 1110°, and so on.
Note: Since, sine is an odd function, the value of sin(-390°) = -sin(390°).

Methods to Find Value of Sin 390 Degrees

The sine function is positive in the 1st quadrant. The value of sin 390° is given as 0.5. We can find the value of sin 390 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 390 Degrees Using Unit Circle

To find the value of sin 390 degrees using the unit circle, represent 390° in the form (1 × 360°) + 30° [∵ 390°>360°] ∵ sine is a periodic function, sin 390° = sin 30°.

• Rotate ‘r’ anticlockwise to form a 30° or 390° angle with the positive x-axis.
• The sin of 390 degrees equals the y-coordinate(0.5) of the point of intersection (0.866, 0.5) of unit circle and r.

Hence the value of sin 390° = y = 0.5

Sin 390° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 390 degrees as:

• ± √(1-cos²(390°))
• ± tan 390°/√(1 + tan²(390°))
• ± 1/√(1 + cot²(390°))
• ± √(sec²(390°) - 1)/sec 390°
• 1/cosec 390°

Note: Since 390° lies in the 1st Quadrant, the final value of sin 390° will be positive.

We can use trigonometric identities to represent sin 390° as,

• sin(180° - 390°) = sin(-210°)
• -sin(180° + 390°) = -sin 570°
• cos(90° - 390°) = cos(-300°)
• -cos(90° + 390°) = -cos 480°

☛ Also Check:

• sin 360 degrees
• sin 90 degrees
• sin 75 degrees
• sin 83 degrees
• sin 88 degrees
• sin 69 degrees

FAQs on Sin 390 Degrees

What is Sin 390 Degrees?

Sin 390 degrees is the value of sine trigonometric function for an angle equal to 390 degrees. The value of sin 390° is 1/2 or 0.5.

How to Find Sin 390° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 390° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(390°))
• ± tan 390°/√(1 + tan²(390°))
• ± 1/√(1 + cot²(390°))
• ± √(sec²(390°) - 1)/sec 390°
• 1/cosec 390°

☛ Also check: trigonometric table

How to Find the Value of Sin 390 Degrees?

The value of sin 390 degrees can be calculated by constructing an angle of 390° with the x-axis, and then finding the coordinates of the corresponding point (0.866, 0.5) on the unit circle. The value of sin 390° is equal to the y-coordinate (0.5). ∴ sin 390° = 0.5.

What is the Value of Sin 390 Degrees in Terms of Tan 390°?

We know, using trig identities, we can write sin 390° as tan 390°/√(1 + tan²(390°)). Here, the value of tan 390° is equal to 0.577350.

What is the Value of Sin 390° in Terms of Cosec 390°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 390° as 1/cosec(390°). The value of cosec 390° is equal to 2.