Sin 50 Degrees

The value of sin 50 degrees is 0.7660444. . .. Sin 50 degrees in radians is written as sin (50° × π/180°), i.e., sin (5π/18) or sin (0.872664. . .). In this article, we will discuss the methods to find the value of sin 50 degrees with examples.

• Sin 50°: 0.7660444. . .
• Sin (-50 degrees): -0.7660444. . .
• Sin 50° in radians: sin (5π/18) or sin (0.8726646 . . .)

What is the Value of Sin 50 Degrees?

The value of sin 50 degrees in decimal is 0.766044443. . .. Sin 50 degrees can also be expressed using the equivalent of the given angle (50 degrees) in radians (0.87266 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 50 degrees = 50° × (π/180°) rad = 5π/18 or 0.8726 . . .
∴ sin 50° = sin(0.8726) = 0.7660444. . .

Explanation:

For sin 50 degrees, the angle 50° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 50° value = 0.7660444. . .
Since the sine function is a periodic function, we can represent sin 50° as, sin 50 degrees = sin(50° + n × 360°), n ∈ Z.
⇒ sin 50° = sin 410° = sin 770°, and so on.
Note: Since, sine is an odd function, the value of sin(-50°) = -sin(50°).

Methods to Find Value of Sin 50 Degrees

The sine function is positive in the 1st quadrant. The value of sin 50° is given as 0.76604. . .. We can find the value of sin 50 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 50 Degrees Using Unit Circle

To find the value of sin 50 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 50° angle with the positive x-axis.
• The sin of 50 degrees equals the y-coordinate(0.766) of the point of intersection (0.6428, 0.766) of unit circle and r.

Hence the value of sin 50° = y = 0.766 (approx)

Sin 50° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 50 degrees as:

• ± √(1-cos²(50°))
• ± tan 50°/√(1 + tan²(50°))
• ± 1/√(1 + cot²(50°))
• ± √(sec²(50°) - 1)/sec 50°
• 1/cosec 50°

Note: Since 50° lies in the 1st Quadrant, the final value of sin 50° will be positive.

We can use trigonometric identities to represent sin 50° as,

• sin(180° - 50°) = sin 130°
• -sin(180° + 50°) = -sin 230°
• cos(90° - 50°) = cos 40°
• -cos(90° + 50°) = -cos 140°

☛ Also Check:

• sin 40 degrees
• sin 15 degrees
• sin 120 degrees
• sin 225 degrees
• sin 250 degrees
• sin 57 degrees

FAQs on Sin 50 Degrees

What is Sin 50 Degrees?

Sin 50 degrees is the value of sine trigonometric function for an angle equal to 50 degrees. The value of sin 50° is 0.766 (approx).

How to Find Sin 50° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 50° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(50°))
• ± tan 50°/√(1 + tan²(50°))
• ± 1/√(1 + cot²(50°))
• ± √(sec²(50°) - 1)/sec 50°
• 1/cosec 50°

☛ Also check: trigonometry table

How to Find the Value of Sin 50 Degrees?

The value of sin 50 degrees can be calculated by constructing an angle of 50° with the x-axis, and then finding the coordinates of the corresponding point (0.6428, 0.766) on the unit circle. The value of sin 50° is equal to the y-coordinate (0.766). ∴ sin 50° = 0.766.

What is the Value of Sin 50 Degrees in Terms of Tan 50°?

We know, using trig identities, we can write sin 50° as tan 50°/√(1 + tan²(50°)). Here, the value of tan 50° is equal to 1.191753.

What is the Exact Value of sin 50 Degrees?

The exact value of sin 50 degrees can be given accurately up to 8 decimal places as 0.76604444.