Sin 104 Degrees

The value of sin 104 degrees is 0.9702957. . .. Sin 104 degrees in radians is written as sin (104° × π/180°), i.e., sin (26π/45) or sin (1.815142. . .). In this article, we will discuss the methods to find the value of sin 104 degrees with examples.

• Sin 104°: 0.9702957. . .
• Sin (-104 degrees): -0.9702957. . .
• Sin 104° in radians: sin (26π/45) or sin (1.8151424 . . .)

What is the Value of Sin 104 Degrees?

The value of sin 104 degrees in decimal is 0.970295726. . .. Sin 104 degrees can also be expressed using the equivalent of the given angle (104 degrees) in radians (1.81514 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 104 degrees = 104° × (π/180°) rad = 26π/45 or 1.8151 . . .
∴ sin 104° = sin(1.8151) = 0.9702957. . .

Explanation:

For sin 104 degrees, the angle 104° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 104° value = 0.9702957. . .
Since the sine function is a periodic function, we can represent sin 104° as, sin 104 degrees = sin(104° + n × 360°), n ∈ Z.
⇒ sin 104° = sin 464° = sin 824°, and so on.
Note: Since, sine is an odd function, the value of sin(-104°) = -sin(104°).

Methods to Find Value of Sin 104 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 104° is given as 0.97029. . .. We can find the value of sin 104 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 104° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 104 degrees as:

• ± √(1-cos²(104°))
• ± tan 104°/√(1 + tan²(104°))
• ± 1/√(1 + cot²(104°))
• ± √(sec²(104°) - 1)/sec 104°
• 1/cosec 104°

Note: Since 104° lies in the 2nd Quadrant, the final value of sin 104° will be positive.

We can use trigonometric identities to represent sin 104° as,

• sin(180° - 104°) = sin 76°
• -sin(180° + 104°) = -sin 284°
• cos(90° - 104°) = cos(-14°)
• -cos(90° + 104°) = -cos 194°

Sin 104 Degrees Using Unit Circle

To find the value of sin 104 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 104° angle with the positive x-axis.
• The sin of 104 degrees equals the y-coordinate(0.9703) of the point of intersection (-0.2419, 0.9703) of unit circle and r.

Hence the value of sin 104° = y = 0.9703 (approx)

☛ Also Check:

• sin 20 degrees
• sin 150 degrees
• sin 35 degrees
• sin 14 degrees
• sin 49 degrees
• sin 27 degrees

FAQs on Sin 104 Degrees

What is Sin 104 Degrees?

Sin 104 degrees is the value of sine trigonometric function for an angle equal to 104 degrees. The value of sin 104° is 0.9703 (approx).

How to Find Sin 104° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 104° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(104°))
• ± tan 104°/√(1 + tan²(104°))
• ± 1/√(1 + cot²(104°))
• ± √(sec²(104°) - 1)/sec 104°
• 1/cosec 104°

☛ Also check: trigonometric table

What is the Value of Sin 104 Degrees in Terms of Tan 104°?

We know, using trig identities, we can write sin 104° as -tan 104°/√(1 + tan²(104°)). Here, the value of tan 104° is equal to -4.010780.

How to Find the Value of Sin 104 Degrees?

The value of sin 104 degrees can be calculated by constructing an angle of 104° with the x-axis, and then finding the coordinates of the corresponding point (-0.2419, 0.9703) on the unit circle. The value of sin 104° is equal to the y-coordinate (0.9703). ∴ sin 104° = 0.9703.

What is the Exact Value of sin 104 Degrees?

The exact value of sin 104 degrees can be given accurately up to 8 decimal places as 0.97029572.