Sin 32 Degrees

The value of sin 32 degrees is 0.5299192. . .. Sin 32 degrees in radians is written as sin (32° × π/180°), i.e., sin (8π/45) or sin (0.558505. . .). In this article, we will discuss the methods to find the value of sin 32 degrees with examples.

• Sin 32°: 0.5299192. . .
• Sin (-32 degrees): -0.5299192. . .
• Sin 32° in radians: sin (8π/45) or sin (0.5585053 . . .)

What is the Value of Sin 32 Degrees?

The value of sin 32 degrees in decimal is 0.529919264. . .. Sin 32 degrees can also be expressed using the equivalent of the given angle (32 degrees) in radians (0.55850 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 32 degrees = 32° × (π/180°) rad = 8π/45 or 0.5585 . . .
∴ sin 32° = sin(0.5585) = 0.5299192. . .

Explanation:

For sin 32 degrees, the angle 32° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 32° value = 0.5299192. . .
Since the sine function is a periodic function, we can represent sin 32° as, sin 32 degrees = sin(32° + n × 360°), n ∈ Z.
⇒ sin 32° = sin 392° = sin 752°, and so on.
Note: Since, sine is an odd function, the value of sin(-32°) = -sin(32°).

Methods to Find Value of Sin 32 Degrees

The sine function is positive in the 1st quadrant. The value of sin 32° is given as 0.52991. . .. We can find the value of sin 32 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sin 32° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 32 degrees as:

• ± √(1-cos²(32°))
• ± tan 32°/√(1 + tan²(32°))
• ± 1/√(1 + cot²(32°))
• ± √(sec²(32°) - 1)/sec 32°
• 1/cosec 32°

Note: Since 32° lies in the 1st Quadrant, the final value of sin 32° will be positive.

We can use trigonometric identities to represent sin 32° as,

• sin(180° - 32°) = sin 148°
• -sin(180° + 32°) = -sin 212°
• cos(90° - 32°) = cos 58°
• -cos(90° + 32°) = -cos 122°

Sin 32 Degrees Using Unit Circle

To find the value of sin 32 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 32° angle with the positive x-axis.
• The sin of 32 degrees equals the y-coordinate(0.5299) of the point of intersection (0.848, 0.5299) of unit circle and r.

Hence the value of sin 32° = y = 0.5299 (approx)

☛ Also Check:

• sin 10 degrees
• sin 35 degrees
• sin 18 degrees
• sin 26 degrees
• sin 170 degrees
• sin 857 degrees

FAQs on Sin 32 Degrees

What is Sin 32 Degrees?

Sin 32 degrees is the value of sine trigonometric function for an angle equal to 32 degrees. The value of sin 32° is 0.5299 (approx).

What is the Value of Sin 32 Degrees in Terms of Cot 32°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 32° can be written as 1/√(1 + cot²(32°)). Here, the value of cot 32° is equal to 1.60033.

How to Find Sin 32° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 32° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(32°))
• ± tan 32°/√(1 + tan²(32°))
• ± 1/√(1 + cot²(32°))
• ± √(sec²(32°) - 1)/sec 32°
• 1/cosec 32°

☛ Also check: trigonometry table

How to Find the Value of Sin 32 Degrees?

The value of sin 32 degrees can be calculated by constructing an angle of 32° with the x-axis, and then finding the coordinates of the corresponding point (0.848, 0.5299) on the unit circle. The value of sin 32° is equal to the y-coordinate (0.5299). ∴ sin 32° = 0.5299.

What is the Value of Sin 32° in Terms of Cosec 32°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 32° as 1/cosec(32°). The value of cosec 32° is equal to 1.88707.