Sin 22 Degrees

The value of sin 22 degrees is 0.3746065. . .. Sin 22 degrees in radians is written as sin (22° × π/180°), i.e., sin (11π/90) or sin (0.383972. . .). In this article, we will discuss the methods to find the value of sin 22 degrees with examples.

• Sin 22°: 0.3746065. . .
• Sin (-22 degrees): -0.3746065. . .
• Sin 22° in radians: sin (11π/90) or sin (0.3839724 . . .)

What is the Value of Sin 22 Degrees?

The value of sin 22 degrees in decimal is 0.374606593. . .. Sin 22 degrees can also be expressed using the equivalent of the given angle (22 degrees) in radians (0.38397 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 22 degrees = 22° × (π/180°) rad = 11π/90 or 0.3839 . . .
∴ sin 22° = sin(0.3839) = 0.3746065. . .

Explanation:

For sin 22 degrees, the angle 22° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 22° value = 0.3746065. . .
Since the sine function is a periodic function, we can represent sin 22° as, sin 22 degrees = sin(22° + n × 360°), n ∈ Z.
⇒ sin 22° = sin 382° = sin 742°, and so on.
Note: Since, sine is an odd function, the value of sin(-22°) = -sin(22°).

Methods to Find Value of Sin 22 Degrees

The sine function is positive in the 1st quadrant. The value of sin 22° is given as 0.37460. . .. We can find the value of sin 22 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 22 Degrees Using Unit Circle

To find the value of sin 22 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 22° angle with the positive x-axis.
• The sin of 22 degrees equals the y-coordinate(0.3746) of the point of intersection (0.9272, 0.3746) of unit circle and r.

Hence the value of sin 22° = y = 0.3746 (approx)

Sin 22° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 22 degrees as:

• ± √(1-cos²(22°))
• ± tan 22°/√(1 + tan²(22°))
• ± 1/√(1 + cot²(22°))
• ± √(sec²(22°) - 1)/sec 22°
• 1/cosec 22°

Note: Since 22° lies in the 1st Quadrant, the final value of sin 22° will be positive.

We can use trigonometric identities to represent sin 22° as,

• sin(180° - 22°) = sin 158°
• -sin(180° + 22°) = -sin 202°
• cos(90° - 22°) = cos 68°
• -cos(90° + 22°) = -cos 112°

☛ Also Check:

• sin 60 degrees
• sin 150 degrees
• sin 270 degrees
• sin 17 degrees
• sin 27 degrees
• sin 1500 degrees

FAQs on Sin 22 Degrees

What is Sin 22 Degrees?

Sin 22 degrees is the value of sine trigonometric function for an angle equal to 22 degrees. The value of sin 22° is 0.3746 (approx).

How to Find Sin 22° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 22° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(22°))
• ± tan 22°/√(1 + tan²(22°))
• ± 1/√(1 + cot²(22°))
• ± √(sec²(22°) - 1)/sec 22°
• 1/cosec 22°

☛ Also check: trigonometry table

What is the Value of Sin 22 Degrees in Terms of Tan 22°?

We know, using trig identities, we can write sin 22° as tan 22°/√(1 + tan²(22°)). Here, the value of tan 22° is equal to 0.404026.

How to Find the Value of Sin 22 Degrees?

The value of sin 22 degrees can be calculated by constructing an angle of 22° with the x-axis, and then finding the coordinates of the corresponding point (0.9272, 0.3746) on the unit circle. The value of sin 22° is equal to the y-coordinate (0.3746). ∴ sin 22° = 0.3746.

What is the Value of Sin 22° in Terms of Sec 22°?

Since the sine function can be represented using the secant function, we can write sin 22° as √(sec²(22°) - 1)/sec 22°. The value of sec 22° is equal to 1.078535.