Sin 17 Degrees

The value of sin 17 degrees is 0.2923717. . .. Sin 17 degrees in radians is written as sin (17° × π/180°), i.e., sin (0.296705. . .). In this article, we will discuss the methods to find the value of sin 17 degrees with examples.

• Sin 17°: 0.2923717. . .
• Sin (-17 degrees): -0.2923717. . .
• Sin 17° in radians: sin (0.2967059 . . .)

What is the Value of Sin 17 Degrees?

The value of sin 17 degrees in decimal is 0.292371704. . .. Sin 17 degrees can also be expressed using the equivalent of the given angle (17 degrees) in radians (0.29670 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 17 degrees = 17° × (π/180°) rad = 0.2967 . . .
∴ sin 17° = sin(0.2967) = 0.2923717. . .

Explanation:

For sin 17 degrees, the angle 17° lies between 0° and 90° (First Quadrant). Since sine function is positive in the first quadrant, thus sin 17° value = 0.2923717. . .
Since the sine function is a periodic function, we can represent sin 17° as, sin 17 degrees = sin(17° + n × 360°), n ∈ Z.
⇒ sin 17° = sin 377° = sin 737°, and so on.
Note: Since, sine is an odd function, the value of sin(-17°) = -sin(17°).

Methods to Find Value of Sin 17 Degrees

The sine function is positive in the 1st quadrant. The value of sin 17° is given as 0.29237. . .. We can find the value of sin 17 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 17 Degrees Using Unit Circle

To find the value of sin 17 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 17° angle with the positive x-axis.
• The sin of 17 degrees equals the y-coordinate(0.2924) of the point of intersection (0.9563, 0.2924) of unit circle and r.

Hence the value of sin 17° = y = 0.2924 (approx)

Sin 17° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 17 degrees as:

• ± √(1-cos²(17°))
• ± tan 17°/√(1 + tan²(17°))
• ± 1/√(1 + cot²(17°))
• ± √(sec²(17°) - 1)/sec 17°
• 1/cosec 17°

Note: Since 17° lies in the 1st Quadrant, the final value of sin 17° will be positive.

We can use trigonometric identities to represent sin 17° as,

• sin(180° - 17°) = sin 163°
• -sin(180° + 17°) = -sin 197°
• cos(90° - 17°) = cos 73°
• -cos(90° + 17°) = -cos 107°

☛ Also Check:

• sin 0 degrees
• sin 2 degrees
• sin 180 degrees
• sin 656 degrees
• sin 46 degrees
• sin 690 degrees

FAQs on Sin 17 Degrees

What is Sin 17 Degrees?

Sin 17 degrees is the value of sine trigonometric function for an angle equal to 17 degrees. The value of sin 17° is 0.2924 (approx).

What is the Value of Sin 17° in Terms of Cosec 17°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 17° as 1/cosec(17°). The value of cosec 17° is equal to 3.42030.

How to Find Sin 17° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 17° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(17°))
• ± tan 17°/√(1 + tan²(17°))
• ± 1/√(1 + cot²(17°))
• ± √(sec²(17°) - 1)/sec 17°
• 1/cosec 17°

☛ Also check: trigonometry table

What is the Value of Sin 17 Degrees in Terms of Tan 17°?

We know, using trig identities, we can write sin 17° as tan 17°/√(1 + tan²(17°)). Here, the value of tan 17° is equal to 0.305730.

How to Find the Value of Sin 17 Degrees?

The value of sin 17 degrees can be calculated by constructing an angle of 17° with the x-axis, and then finding the coordinates of the corresponding point (0.9563, 0.2924) on the unit circle. The value of sin 17° is equal to the y-coordinate (0.2924). ∴ sin 17° = 0.2924.