Sin 250 Degrees

The value of sin 250 degrees is -0.9396926. . .. Sin 250 degrees in radians is written as sin (250° × π/180°), i.e., sin (25π/18) or sin (4.363323. . .). In this article, we will discuss the methods to find the value of sin 250 degrees with examples.

• Sin 250°: -0.9396926. . .
• Sin (-250 degrees): 0.9396926. . .
• Sin 250° in radians: sin (25π/18) or sin (4.3633231 . . .)

What is the Value of Sin 250 Degrees?

The value of sin 250 degrees in decimal is -0.939692620. . .. Sin 250 degrees can also be expressed using the equivalent of the given angle (250 degrees) in radians (4.36332 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 250 degrees = 250° × (π/180°) rad = 25π/18 or 4.3633 . . .
∴ sin 250° = sin(4.3633) = -0.9396926. . .

Explanation:

For sin 250 degrees, the angle 250° lies between 180° and 270° (Third Quadrant). Since sine function is negative in the third quadrant, thus sin 250° value = -0.9396926. . .
Since the sine function is a periodic function, we can represent sin 250° as, sin 250 degrees = sin(250° + n × 360°), n ∈ Z.
⇒ sin 250° = sin 610° = sin 970°, and so on.
Note: Since, sine is an odd function, the value of sin(-250°) = -sin(250°).

Methods to Find Value of Sin 250 Degrees

The sine function is negative in the 3rd quadrant. The value of sin 250° is given as -0.93969. . .. We can find the value of sin 250 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 250° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 250 degrees as:

• ± √(1-cos²(250°))
• ± tan 250°/√(1 + tan²(250°))
• ± 1/√(1 + cot²(250°))
• ± √(sec²(250°) - 1)/sec 250°
• 1/cosec 250°

Note: Since 250° lies in the 3rd Quadrant, the final value of sin 250° will be negative.

We can use trigonometric identities to represent sin 250° as,

• sin(180° - 250°) = sin(-70°)
• -sin(180° + 250°) = -sin 430°
• cos(90° - 250°) = cos(-160°)
• -cos(90° + 250°) = -cos 340°

Sin 250 Degrees Using Unit Circle

To find the value of sin 250 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 250° angle with the positive x-axis.
• The sin of 250 degrees equals the y-coordinate(-0.9397) of the point of intersection (-0.342, -0.9397) of unit circle and r.

Hence the value of sin 250° = y = -0.9397 (approx)

☛ Also Check:

• sin 150 degrees
• sin 270 degrees
• sin 75 degrees
• sin 933 degrees
• sin 67 degrees
• sin 158 degrees

FAQs on Sin 250 Degrees

What is Sin 250 Degrees?

Sin 250 degrees is the value of sine trigonometric function for an angle equal to 250 degrees. The value of sin 250° is -0.9397 (approx).

What is the Value of Sin 250 Degrees in Terms of Cot 250°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 250° can be written as -1/√(1 + cot²(250°)). Here, the value of cot 250° is equal to 0.36397.

What is the Exact Value of sin 250 Degrees?

The exact value of sin 250 degrees can be given accurately up to 8 decimal places as -0.93969262.

How to Find Sin 250° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 250° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(250°))
• ± tan 250°/√(1 + tan²(250°))
• ± 1/√(1 + cot²(250°))
• ± √(sec²(250°) - 1)/sec 250°
• 1/cosec 250°

☛ Also check: trigonometric table

How to Find the Value of Sin 250 Degrees?

The value of sin 250 degrees can be calculated by constructing an angle of 250° with the x-axis, and then finding the coordinates of the corresponding point (-0.342, -0.9397) on the unit circle. The value of sin 250° is equal to the y-coordinate (-0.9397). ∴ sin 250° = -0.9397.