Sin 37 Degrees

The value of sin 37 degrees is 0.6018150. . .. Sin 37 degrees in radians is written as sin (37° × π/180°), i.e., sin (0.645771. . .). In this article, we will discuss the methods to find the value of sin 37 degrees with examples.

• Sin 37°: 0.6018150. . .
• Sin (-37 degrees): -0.6018150. . .
• Sin 37° in radians: sin (0.6457718 . . .)

What is the Value of Sin 37 Degrees?

The value of sin 37 degrees in decimal is 0.601815023. . .. Sin 37 degrees can also be expressed using the equivalent of the given angle (37 degrees) in radians (0.64577 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 37 degrees = 37° × (π/180°) rad = 0.6457 . . .
∴ sin 37° = sin(0.6457) = 0.6018150. . .

Explanation:

For sin 37 degrees, the angle 37° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 37° value = 0.6018150. . .
Since the sine function is a periodic function, we can represent sin 37° as, sin 37 degrees = sin(37° + n × 360°), n ∈ Z.
⇒ sin 37° = sin 397° = sin 757°, and so on.
Note: Since, sine is an odd function, the value of sin(-37°) = -sin(37°).

Methods to Find Value of Sin 37 Degrees

The sine function is positive in the 1st quadrant. The value of sin 37° is given as 0.60181. . .. We can find the value of sin 37 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 37° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 37 degrees as:

• ± √(1-cos²(37°))
• ± tan 37°/√(1 + tan²(37°))
• ± 1/√(1 + cot²(37°))
• ± √(sec²(37°) - 1)/sec 37°
• 1/cosec 37°

Note: Since 37° lies in the 1st Quadrant, the final value of sin 37° will be positive.

We can use trigonometric identities to represent sin 37° as,

• sin(180° - 37°) = sin 143°
• -sin(180° + 37°) = -sin 217°
• cos(90° - 37°) = cos 53°
• -cos(90° + 37°) = -cos 127°

Sin 37 Degrees Using Unit Circle

To find the value of sin 37 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 37° angle with the positive x-axis.
• The sin of 37 degrees equals the y-coordinate(0.6018) of the point of intersection (0.7986, 0.6018) of unit circle and r.

Hence the value of sin 37° = y = 0.6018 (approx)

☛ Also Check:

• sin 270 degrees
• sin 2 degrees
• sin 20 degrees
• sin 16 degrees
• sin 83 degrees
• sin 1000 degrees

FAQs on Sin 37 Degrees

What is Sin 37 Degrees?

Sin 37 degrees is the value of sine trigonometric function for an angle equal to 37 degrees. The value of sin 37° is 0.6018 (approx).

What is the Value of Sin 37° in Terms of Cosec 37°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 37° as 1/cosec(37°). The value of cosec 37° is equal to 1.66164.

How to Find the Value of Sin 37 Degrees?

The value of sin 37 degrees can be calculated by constructing an angle of 37° with the x-axis, and then finding the coordinates of the corresponding point (0.7986, 0.6018) on the unit circle. The value of sin 37° is equal to the y-coordinate (0.6018). ∴ sin 37° = 0.6018.

How to Find Sin 37° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 37° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(37°))
• ± tan 37°/√(1 + tan²(37°))
• ± 1/√(1 + cot²(37°))
• ± √(sec²(37°) - 1)/sec 37°
• 1/cosec 37°

☛ Also check: trigonometric table

What is the Value of Sin 37 Degrees in Terms of Cos 37°?

Using trigonometric identities, we can write sin 37° in terms of cos 37° as, sin(37°) = √(1-cos²(37°)). Here, the value of cos 37° is equal to 0.7986355.