Sin 170 Degrees

The value of sin 170 degrees is 0.1736481. . .. Sin 170 degrees in radians is written as sin (170° × π/180°), i.e., sin (17π/18) or sin (2.967059. . .). In this article, we will discuss the methods to find the value of sin 170 degrees with examples.

• Sin 170°: 0.1736481. . .
• Sin (-170 degrees): -0.1736481. . .
• Sin 170° in radians: sin (17π/18) or sin (2.9670597 . . .)

What is the Value of Sin 170 Degrees?

The value of sin 170 degrees in decimal is 0.173648177. . .. Sin 170 degrees can also be expressed using the equivalent of the given angle (170 degrees) in radians (2.96705 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 170 degrees = 170° × (π/180°) rad = 17π/18 or 2.9670 . . .
∴ sin 170° = sin(2.9670) = 0.1736481. . .

Explanation:

For sin 170 degrees, the angle 170° lies between 90° and 180° (Second Quadrant). Since sine function is positive in the second quadrant, thus sin 170° value = 0.1736481. . .
Since the sine function is a periodic function, we can represent sin 170° as, sin 170 degrees = sin(170° + n × 360°), n ∈ Z.
⇒ sin 170° = sin 530° = sin 890°, and so on.
Note: Since, sine is an odd function, the value of sin(-170°) = -sin(170°).

Methods to Find Value of Sin 170 Degrees

The sine function is positive in the 2nd quadrant. The value of sin 170° is given as 0.17364. . .. We can find the value of sin 170 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sin 170 Degrees Using Unit Circle

To find the value of sin 170 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form a 170° angle with the positive x-axis.
• The sin of 170 degrees equals the y-coordinate(0.1736) of the point of intersection (-0.9848, 0.1736) of unit circle and r.

Hence the value of sin 170° = y = 0.1736 (approx)

Sin 170° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sin 170 degrees as:

• ± √(1-cos²(170°))
• ± tan 170°/√(1 + tan²(170°))
• ± 1/√(1 + cot²(170°))
• ± √(sec²(170°) - 1)/sec 170°
• 1/cosec 170°

Note: Since 170° lies in the 2nd Quadrant, the final value of sin 170° will be positive.

We can use trigonometric identities to represent sin 170° as,

• sin(180° - 170°) = sin 10°
• -sin(180° + 170°) = -sin 350°
• cos(90° - 170°) = cos(-80°)
• -cos(90° + 170°) = -cos 260°

☛ Also Check:

• sin 270 degrees
• sin 135 degrees
• sin 75 degrees
• sin 47 degrees
• sin 720 degrees
• sin 28 degrees

FAQs on Sin 170 Degrees

What is Sin 170 Degrees?

Sin 170 degrees is the value of sine trigonometric function for an angle equal to 170 degrees. The value of sin 170° is 0.1736 (approx).

What is the Value of Sin 170 Degrees in Terms of Tan 170°?

We know, using trig identities, we can write sin 170° as -tan 170°/√(1 + tan²(170°)). Here, the value of tan 170° is equal to -0.176326.

How to Find the Value of Sin 170 Degrees?

The value of sin 170 degrees can be calculated by constructing an angle of 170° with the x-axis, and then finding the coordinates of the corresponding point (-0.9848, 0.1736) on the unit circle. The value of sin 170° is equal to the y-coordinate (0.1736). ∴ sin 170° = 0.1736.

What is the Value of Sin 170° in Terms of Cosec 170°?

Since the cosecant function is the reciprocal of the sine function, we can write sin 170° as 1/cosec(170°). The value of cosec 170° is equal to 5.75877.

How to Find Sin 170° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sin 170° can be given in terms of other trigonometric functions as:

• ± √(1-cos²(170°))
• ± tan 170°/√(1 + tan²(170°))
• ± 1/√(1 + cot²(170°))
• ± √(sec²(170°) - 1)/sec 170°
• 1/cosec 170°

☛ Also check: trigonometry table