Sin 34 Degrees

The value of sin 34 degrees is 0.5591929. . .. Sin 34 degrees in radians is written as sin (34° × π/180°), i.e., sin (17π/90) or sin (0.593411. . .). In this article, we will discuss the methods to find the value of sin 34 degrees with examples.

• Sin 34°: 0.5591929. . .
• Sin (-34 degrees): -0.5591929. . .
• Sin 34° in radians: sin (17π/90) or sin (0.5934119 . . .)

What is the Value of Sin 34 Degrees?

The value of sin 34 degrees in decimal is 0.559192903. . .. Sin 34 degrees can also be expressed using the equivalent of the given angle (34 degrees) in radians (0.59341 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 34 degrees = 34° × (π/180°) rad = 17π/90 or 0.5934 . . .
∴ sin 34° = sin(0.5934) = 0.5591929. . .

Explanation:

For sin 34 degrees, the angle 34° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 34° value = 0.5591929. . .
Since the sine function is a periodic function, we can represent sin 34° as, sin 34 degrees = sin(34° + n × 360°), n ∈ Z.
⇒ sin 34° = sin 394° = sin 754°, and so on.
Note: Since, sine is an odd function, the value of sin(-34°) = -sin(34°).

Methods to Find Value of Sin 34 Degrees

The sine function is positive in the 1st quadrant. The value of sin 34° is given as 0.55919. . .. We can find the value of sin 34 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 34° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 34 degrees as:

• ± √(1-cos²(34°))
• ± tan 34°/√(1 + tan²(34°))
• ± 1/√(1 + cot²(34°))
• ± √(sec²(34°) - 1)/sec 34°
• 1/cosec 34°

Note: Since 34° lies in the 1st Quadrant, the final value of sin 34° will be positive.

We can use trigonometric identities to represent sin 34° as,

• sin(180° - 34°) = sin 146°
• -sin(180° + 34°) = -sin 214°
• cos(90° - 34°) = cos 56°
• -cos(90° + 34°) = -cos 124°

Sin 34 Degrees Using Unit Circle

To find the value of sin 34 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 34° angle with the positive x-axis.
• The sin of 34 degrees equals the y-coordinate(0.5592) of the point of intersection (0.829, 0.5592) of unit circle and r.

Hence the value of sin 34° = y = 0.5592 (approx)

☛ Also Check:

• sin 120 degrees
• sin 360 degrees
• sin 37 degrees
• sin 27 degrees
• sin 47 degrees
• sin 31 degrees

FAQs on Sin 34 Degrees

What is Sin 34 Degrees?

Sin 34 degrees is the value of sine trigonometric function for an angle equal to 34 degrees. The value of sin 34° is 0.5592 (approx).

What is the Value of Sin 34 Degrees in Terms of Tan 34°?

We know, using trig identities, we can write sin 34° as tan 34°/√(1 + tan²(34°)). Here, the value of tan 34° is equal to 0.674508.

How to Find Sin 34° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 34° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(34°))
• ± tan 34°/√(1 + tan²(34°))
• ± 1/√(1 + cot²(34°))
• ± √(sec²(34°) - 1)/sec 34°
• 1/cosec 34°

☛ Also check: trigonometry table

How to Find the Value of Sin 34 Degrees?

The value of sin 34 degrees can be calculated by constructing an angle of 34° with the x-axis, and then finding the coordinates of the corresponding point (0.829, 0.5592) on the unit circle. The value of sin 34° is equal to the y-coordinate (0.5592). ∴ sin 34° = 0.5592.

What is the Value of Sin 34° in Terms of Cosec 34°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 34° as 1/cosec(34°). The value of cosec 34° is equal to 1.78829.