Sin 47 Degrees

The value of sin 47 degrees is 0.7313537. . .. Sin 47 degrees in radians is written as sin (47° × π/180°), i.e., sin (0.820304. . .). In this article, we will discuss the methods to find the value of sin 47 degrees with examples.

• Sin 47°: 0.7313537. . .
• Sin (-47 degrees): -0.7313537. . .
• Sin 47° in radians: sin (0.8203047 . . .)

What is the Value of Sin 47 Degrees?

The value of sin 47 degrees in decimal is 0.731353701. . .. Sin 47 degrees can also be expressed using the equivalent of the given angle (47 degrees) in radians (0.82030 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 47 degrees = 47° × (π/180°) rad = 0.8203 . . .
∴ sin 47° = sin(0.8203) = 0.7313537. . .

Explanation:

For sin 47 degrees, the angle 47° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 47° value = 0.7313537. . .
Since the sine function is a periodic function, we can represent sin 47° as, sin 47 degrees = sin(47° + n × 360°), n ∈ Z.
⇒ sin 47° = sin 407° = sin 767°, and so on.
Note: Since, sine is an odd function, the value of sin(-47°) = -sin(47°).

Methods to Find Value of Sin 47 Degrees

The sine function is positive in the 1st quadrant. The value of sin 47° is given as 0.73135. . .. We can find the value of sin 47 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 47 Degrees Using Unit Circle

To find the value of sin 47 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 47° angle with the positive x-axis.
• The sin of 47 degrees equals the y-coordinate(0.7314) of the point of intersection (0.682, 0.7314) of unit circle and r.

Hence the value of sin 47° = y = 0.7314 (approx)

Sin 47° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 47 degrees as:

• ± √(1-cos²(47°))
• ± tan 47°/√(1 + tan²(47°))
• ± 1/√(1 + cot²(47°))
• ± √(sec²(47°) - 1)/sec 47°
• 1/cosec 47°

Note: Since 47° lies in the 1st Quadrant, the final value of sin 47° will be positive.

We can use trigonometric identities to represent sin 47° as,

• sin(180° - 47°) = sin 133°
• -sin(180° + 47°) = -sin 227°
• cos(90° - 47°) = cos 43°
• -cos(90° + 47°) = -cos 137°

☛ Also Check:

• sin 53 degrees
• sin 75 degrees
• sin 180 degrees
• sin 66 degrees
• sin 660 degrees
• sin 127 degrees

FAQs on Sin 47 Degrees

What is Sin 47 Degrees?

Sin 47 degrees is the value of sine trigonometric function for an angle equal to 47 degrees. The value of sin 47° is 0.7314 (approx).

How to Find the Value of Sin 47 Degrees?

The value of sin 47 degrees can be calculated by constructing an angle of 47° with the x-axis, and then finding the coordinates of the corresponding point (0.682, 0.7314) on the unit circle. The value of sin 47° is equal to the y-coordinate (0.7314). ∴ sin 47° = 0.7314.

How to Find Sin 47° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 47° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(47°))
• ± tan 47°/√(1 + tan²(47°))
• ± 1/√(1 + cot²(47°))
• ± √(sec²(47°) - 1)/sec 47°
• 1/cosec 47°

☛ Also check: trigonometry table

What is the Value of Sin 47 Degrees in Terms of Cos 47°?

Using trigonometric identities, we can write sin 47° in terms of cos 47° as, sin(47°) = √(1-cos²(47°)). Here, the value of cos 47° is equal to 0.6819983.

What is the Value of Sin 47° in Terms of Sec 47°?

Since the sine function can be represented using the secant function, we can write sin 47° as √(sec²(47°) - 1)/sec 47°. The value of sec 47° is equal to 1.466279.