Sin 38 Degrees
The value of sin 38 degrees is 0.6156614. . .. Sin 38 degrees in radians is written as sin (38° × π/180°), i.e., sin (19π/90) or sin (0.663225. . .). In this article, we will discuss the methods to find the value of sin 38 degrees with examples.
- Sin 38°: 0.6156614. . .
- Sin (-38 degrees): -0.6156614. . .
- Sin 38° in radians: sin (19π/90) or sin (0.6632251 . . .)
What is the Value of Sin 38 Degrees?
The value of sin 38 degrees in decimal is 0.615661475. . .. Sin 38 degrees can also be expressed using the equivalent of the given angle (38 degrees) in radians (0.66322 . . .).
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 38 degrees = 38° × (π/180°) rad = 19π/90 or 0.6632 . . .
∴ sin 38° = sin(0.6632) = 0.6156614. . .
Explanation:
For sin 38 degrees, the angle 38° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 38° value = 0.6156614. . .
Since the sine function is a periodic function, we can represent sin 38° as, sin 38 degrees = sin(38° + n × 360°), n ∈ Z.
⇒ sin 38° = sin 398° = sin 758°, and so on.
Note: Since, sine is an odd function, the value of sin(-38°) = -sin(38°).
Methods to Find Value of Sin 38 Degrees
The sine function is positive in the 1st quadrant. The value of sin 38° is given as 0.61566. . .. We can find the value of sin 38 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Sin 38° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sin 38 degrees as:
- ± √(1-cos²(38°))
- ± tan 38°/√(1 + tan²(38°))
- ± 1/√(1 + cot²(38°))
- ± √(sec²(38°) - 1)/sec 38°
- 1/cosec 38°
Note: Since 38° lies in the 1st Quadrant, the final value of sin 38° will be positive.
We can use trigonometric identities to represent sin 38° as,
- sin(180° - 38°) = sin 142°
- -sin(180° + 38°) = -sin 218°
- cos(90° - 38°) = cos 52°
- -cos(90° + 38°) = -cos 128°
Sin 38 Degrees Using Unit Circle
To find the value of sin 38 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form a 38° angle with the positive x-axis.
- The sin of 38 degrees equals the y-coordinate(0.6157) of the point of intersection (0.788, 0.6157) of unit circle and r.
Hence the value of sin 38° = y = 0.6157 (approx)
☛ Also Check:
FAQs on Sin 38 Degrees
What is Sin 38 Degrees?
Sin 38 degrees is the value of sine trigonometric function for an angle equal to 38 degrees. The value of sin 38° is 0.6157 (approx).
What is the Value of Sin 38 Degrees in Terms of Cot 38°?
We can represent the sine function in terms of the cotangent function using trig identities, sin 38° can be written as 1/√(1 + cot²(38°)). Here, the value of cot 38° is equal to 1.27994.
How to Find Sin 38° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sin 38° can be given in terms of other trigonometric functions as:
- ± √(1-cos²(38°))
- ± tan 38°/√(1 + tan²(38°))
- ± 1/√(1 + cot²(38°))
- ± √(sec²(38°) - 1)/sec 38°
- 1/cosec 38°
☛ Also check: trigonometry table
How to Find the Value of Sin 38 Degrees?
The value of sin 38 degrees can be calculated by constructing an angle of 38° with the x-axis, and then finding the coordinates of the corresponding point (0.788, 0.6157) on the unit circle. The value of sin 38° is equal to the y-coordinate (0.6157). ∴ sin 38° = 0.6157.
What is the Value of Sin 38° in Terms of Cosec 38°?
Since the cosecant function is the reciprocal of the sine function, we can write sin 38° as 1/cosec(38°). The value of cosec 38° is equal to 1.62426.