Sin 52 Degrees

The value of sin 52 degrees is 0.7880107. . .. Sin 52 degrees in radians is written as sin (52° × π/180°), i.e., sin (13π/45) or sin (0.907571. . .). In this article, we will discuss the methods to find the value of sin 52 degrees with examples.

• Sin 52°: 0.7880107. . .
• Sin (-52 degrees): -0.7880107. . .
• Sin 52° in radians: sin (13π/45) or sin (0.9075712 . . .)

What is the Value of Sin 52 Degrees?

The value of sin 52 degrees in decimal is 0.788010753. . .. Sin 52 degrees can also be expressed using the equivalent of the given angle (52 degrees) in radians (0.90757 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 52 degrees = 52° × (π/180°) rad = 13π/45 or 0.9075 . . .
∴ sin 52° = sin(0.9075) = 0.7880107. . .

Explanation:

For sin 52 degrees, the angle 52° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 52° value = 0.7880107. . .
Since the sine function is a periodic function, we can represent sin 52° as, sin 52 degrees = sin(52° + n × 360°), n ∈ Z.
⇒ sin 52° = sin 412° = sin 772°, and so on.
Note: Since, sine is an odd function, the value of sin(-52°) = -sin(52°).

Methods to Find Value of Sin 52 Degrees

The sine function is positive in the 1st quadrant. The value of sin 52° is given as 0.78801. . .. We can find the value of sin 52 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 52° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 52 degrees as:

• ± √(1-cos²(52°))
• ± tan 52°/√(1 + tan²(52°))
• ± 1/√(1 + cot²(52°))
• ± √(sec²(52°) - 1)/sec 52°
• 1/cosec 52°

Note: Since 52° lies in the 1st Quadrant, the final value of sin 52° will be positive.

We can use trigonometric identities to represent sin 52° as,

• sin(180° - 52°) = sin 128°
• -sin(180° + 52°) = -sin 232°
• cos(90° - 52°) = cos 38°
• -cos(90° + 52°) = -cos 142°

Sin 52 Degrees Using Unit Circle

To find the value of sin 52 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 52° angle with the positive x-axis.
• The sin of 52 degrees equals the y-coordinate(0.788) of the point of intersection (0.6157, 0.788) of unit circle and r.

Hence the value of sin 52° = y = 0.788 (approx)

☛ Also Check:

• sin 0 degrees
• sin 3 degrees
• sin 50 degrees
• sin 95 degrees
• sin 405 degrees
• sin 390 degrees

FAQs on Sin 52 Degrees

What is Sin 52 Degrees?

Sin 52 degrees is the value of sine trigonometric function for an angle equal to 52 degrees. The value of sin 52° is 0.788 (approx).

How to Find the Value of Sin 52 Degrees?

The value of sin 52 degrees can be calculated by constructing an angle of 52° with the x-axis, and then finding the coordinates of the corresponding point (0.6157, 0.788) on the unit circle. The value of sin 52° is equal to the y-coordinate (0.788). ∴ sin 52° = 0.788.

What is the Value of Sin 52° in Terms of Sec 52°?

Since the sine function can be represented using the secant function, we can write sin 52° as √(sec²(52°) - 1)/sec 52°. The value of sec 52° is equal to 1.624269.

How to Find Sin 52° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 52° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(52°))
• ± tan 52°/√(1 + tan²(52°))
• ± 1/√(1 + cot²(52°))
• ± √(sec²(52°) - 1)/sec 52°
• 1/cosec 52°

☛ Also check: trigonometry table

What is the Value of Sin 52 Degrees in Terms of Cot 52°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 52° can be written as 1/√(1 + cot²(52°)). Here, the value of cot 52° is equal to 0.78128.