Sin 33 Degrees

The value of sin 33 degrees is 0.5446390. . .. Sin 33 degrees in radians is written as sin (33° × π/180°), i.e., sin (11π/60) or sin (0.575958. . .). In this article, we will discuss the methods to find the value of sin 33 degrees with examples.

• Sin 33°: 0.5446390. . .
• Sin (-33 degrees): -0.5446390. . .
• Sin 33° in radians: sin (11π/60) or sin (0.5759586 . . .)

What is the Value of Sin 33 Degrees?

The value of sin 33 degrees in decimal is 0.544639035. . .. Sin 33 degrees can also be expressed using the equivalent of the given angle (33 degrees) in radians (0.57595 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 33 degrees = 33° × (π/180°) rad = 11π/60 or 0.5759 . . .
∴ sin 33° = sin(0.5759) = 0.5446390. . .

Explanation:

For sin 33 degrees, the angle 33° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 33° value = 0.5446390. . .
Since the sine function is a periodic function, we can represent sin 33° as, sin 33 degrees = sin(33° + n × 360°), n ∈ Z.
⇒ sin 33° = sin 393° = sin 753°, and so on.
Note: Since, sine is an odd function, the value of sin(-33°) = -sin(33°).

Methods to Find Value of Sin 33 Degrees

The sine function is positive in the 1st quadrant. The value of sin 33° is given as 0.54463. . .. We can find the value of sin 33 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 33 Degrees Using Unit Circle

To find the value of sin 33 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 33° angle with the positive x-axis.
• The sin of 33 degrees equals the y-coordinate(0.5446) of the point of intersection (0.8387, 0.5446) of unit circle and r.

Hence the value of sin 33° = y = 0.5446 (approx)

Sin 33° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 33 degrees as:

• ± √(1-cos²(33°))
• ± tan 33°/√(1 + tan²(33°))
• ± 1/√(1 + cot²(33°))
• ± √(sec²(33°) - 1)/sec 33°
• 1/cosec 33°

Note: Since 33° lies in the 1st Quadrant, the final value of sin 33° will be positive.

We can use trigonometric identities to represent sin 33° as,

• sin(180° - 33°) = sin 147°
• -sin(180° + 33°) = -sin 213°
• cos(90° - 33°) = cos 57°
• -cos(90° + 33°) = -cos 123°

☛ Also Check:

• sin 60 degrees
• sin 10 degrees
• sin 3 degrees
• sin 210 degrees
• sin 22 degrees
• sin 46 degrees

FAQs on Sin 33 Degrees

What is Sin 33 Degrees?

Sin 33 degrees is the value of sine trigonometric function for an angle equal to 33 degrees. The value of sin 33° is 0.5446 (approx).

How to Find the Value of Sin 33 Degrees?

The value of sin 33 degrees can be calculated by constructing an angle of 33° with the x-axis, and then finding the coordinates of the corresponding point (0.8387, 0.5446) on the unit circle. The value of sin 33° is equal to the y-coordinate (0.5446). ∴ sin 33° = 0.5446.

How to Find Sin 33° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 33° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(33°))
• ± tan 33°/√(1 + tan²(33°))
• ± 1/√(1 + cot²(33°))
• ± √(sec²(33°) - 1)/sec 33°
• 1/cosec 33°

☛ Also check: trigonometric table

What is the Value of Sin 33° in Terms of Cosec 33°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 33° as 1/cosec(33°). The value of cosec 33° is equal to 1.83607.

What is the Value of Sin 33 Degrees in Terms of Cot 33°?

We can represent the sine function in terms of the cotangent function using trig identities, sin 33° can be written as 1/√(1 + cot²(33°)). Here, the value of cot 33° is equal to 1.53986.