Sin 13 Degrees

The value of sin 13 degrees is 0.2249510. . .. Sin 13 degrees in radians is written as sin (13° × π/180°), i.e., sin (0.226892. . .). In this article, we will discuss the methods to find the value of sin 13 degrees with examples.

• Sin 13°: 0.2249510. . .
• Sin (-13 degrees): -0.2249510. . .
• Sin 13° in radians: sin (0.2268928 . . .)

What is the Value of Sin 13 Degrees?

The value of sin 13 degrees in decimal is 0.224951054. . .. Sin 13 degrees can also be expressed using the equivalent of the given angle (13 degrees) in radians (0.22689 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 13 degrees = 13° × (π/180°) rad = 0.2268 . . .
∴ sin 13° = sin(0.2268) = 0.2249510. . .

Explanation:

For sin 13 degrees, the angle 13° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 13° value = 0.2249510. . .
Since the sine function is a periodic function, we can represent sin 13° as, sin 13 degrees = sin(13° + n × 360°), n ∈ Z.
⇒ sin 13° = sin 373° = sin 733°, and so on.
Note: Since, sine is an odd function, the value of sin(-13°) = -sin(13°).

Methods to Find Value of Sin 13 Degrees

The sine function is positive in the 1st quadrant. The value of sin 13° is given as 0.22495. . .. We can find the value of sin 13 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 13 Degrees Using Unit Circle

To find the value of sin 13 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 13° angle with the positive x-axis.
• The sin of 13 degrees equals the y-coordinate(0.225) of the point of intersection (0.9744, 0.225) of unit circle and r.

Hence the value of sin 13° = y = 0.225 (approx)

Sin 13° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 13 degrees as:

• ± √(1-cos²(13°))
• ± tan 13°/√(1 + tan²(13°))
• ± 1/√(1 + cot²(13°))
• ± √(sec²(13°) - 1)/sec 13°
• 1/cosec 13°

Note: Since 13° lies in the 1st Quadrant, the final value of sin 13° will be positive.

We can use trigonometric identities to represent sin 13° as,

• sin(180° - 13°) = sin 167°
• -sin(180° + 13°) = -sin 193°
• cos(90° - 13°) = cos 77°
• -cos(90° + 13°) = -cos 103°

☛ Also Check:

• sin 18 degrees
• sin 2 degrees
• sin 60 degrees
• sin 144 degrees
• sin 25 degrees
• sin 127 degrees

FAQs on Sin 13 Degrees

What is Sin 13 Degrees?

Sin 13 degrees is the value of sine trigonometric function for an angle equal to 13 degrees. The value of sin 13° is 0.225 (approx).

What is the Value of Sin 13 Degrees in Terms of Tan 13°?

We know, using trig identities, we can write sin 13° as tan 13°/√(1 + tan²(13°)). Here, the value of tan 13° is equal to 0.230868.

What is the Value of Sin 13° in Terms of Sec 13°?

Since the sine function can be represented using the secant function, we can write sin 13° as √(sec²(13°) - 1)/sec 13°. The value of sec 13° is equal to 1.026304.

How to Find the Value of Sin 13 Degrees?

The value of sin 13 degrees can be calculated by constructing an angle of 13° with the x-axis, and then finding the coordinates of the corresponding point (0.9744, 0.225) on the unit circle. The value of sin 13° is equal to the y-coordinate (0.225). ∴ sin 13° = 0.225.

How to Find Sin 13° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 13° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(13°))
• ± tan 13°/√(1 + tan²(13°))
• ± 1/√(1 + cot²(13°))
• ± √(sec²(13°) - 1)/sec 13°
• 1/cosec 13°

☛ Also check: trigonometric table