Sin 48 Degrees

The value of sin 48 degrees is 0.7431448. . .. Sin 48 degrees in radians is written as sin (48° × π/180°), i.e., sin (4π/15) or sin (0.837758. . .). In this article, we will discuss the methods to find the value of sin 48 degrees with examples.

• Sin 48°: 0.7431448. . .
• Sin (-48 degrees): -0.7431448. . .
• Sin 48° in radians: sin (4π/15) or sin (0.8377580 . . .)

What is the Value of Sin 48 Degrees?

The value of sin 48 degrees in decimal is 0.743144825. . .. Sin 48 degrees can also be expressed using the equivalent of the given angle (48 degrees) in radians (0.83775 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 48 degrees = 48° × (π/180°) rad = 4π/15 or 0.8377 . . .
∴ sin 48° = sin(0.8377) = 0.7431448. . .

Explanation:

For sin 48 degrees, the angle 48° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 48° value = 0.7431448. . .
Since the sine function is a periodic function, we can represent sin 48° as, sin 48 degrees = sin(48° + n × 360°), n ∈ Z.
⇒ sin 48° = sin 408° = sin 768°, and so on.
Note: Since, sine is an odd function, the value of sin(-48°) = -sin(48°).

Methods to Find Value of Sin 48 Degrees

The sine function is positive in the 1st quadrant. The value of sin 48° is given as 0.74314. . .. We can find the value of sin 48 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 48 Degrees Using Unit Circle

To find the value of sin 48 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 48° angle with the positive x-axis.
• The sin of 48 degrees equals the y-coordinate(0.7431) of the point of intersection (0.6691, 0.7431) of unit circle and r.

Hence the value of sin 48° = y = 0.7431 (approx)

Sin 48° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 48 degrees as:

• ± √(1-cos²(48°))
• ± tan 48°/√(1 + tan²(48°))
• ± 1/√(1 + cot²(48°))
• ± √(sec²(48°) - 1)/sec 48°
• 1/cosec 48°

Note: Since 48° lies in the 1st Quadrant, the final value of sin 48° will be positive.

We can use trigonometric identities to represent sin 48° as,

• sin(180° - 48°) = sin 132°
• -sin(180° + 48°) = -sin 228°
• cos(90° - 48°) = cos 42°
• -cos(90° + 48°) = -cos 138°

☛ Also Check:

• sin 15 degrees
• sin 10 degrees
• sin 18 degrees
• sin 930 degrees
• sin 31 degrees
• sin 33 degrees

FAQs on Sin 48 Degrees

What is Sin 48 Degrees?

Sin 48 degrees is the value of sine trigonometric function for an angle equal to 48 degrees. The value of sin 48° is 0.7431 (approx).

What is the Value of Sin 48 Degrees in Terms of Tan 48°?

We know, using trig identities, we can write sin 48° as tan 48°/√(1 + tan²(48°)). Here, the value of tan 48° is equal to 1.110612.

How to Find Sin 48° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 48° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(48°))
• ± tan 48°/√(1 + tan²(48°))
• ± 1/√(1 + cot²(48°))
• ± √(sec²(48°) - 1)/sec 48°
• 1/cosec 48°

☛ Also check: trigonometry table

How to Find the Value of Sin 48 Degrees?

The value of sin 48 degrees can be calculated by constructing an angle of 48° with the x-axis, and then finding the coordinates of the corresponding point (0.6691, 0.7431) on the unit circle. The value of sin 48° is equal to the y-coordinate (0.7431). ∴ sin 48° = 0.7431.

What is the Exact Value of sin 48 Degrees?

The exact value of sin 48 degrees can be given accurately up to 8 decimal places as 0.74314482.