Cos 160 Degrees

The value of cos 160 degrees is -0.9396926. . .. Cos 160 degrees in radians is written as cos (160° × π/180°), i.e., cos (8π/9) or cos (2.792526. . .). In this article, we will discuss the methods to find the value of cos 160 degrees with examples.

• Cos 160°: -0.9396926. . .
• Cos (-160 degrees): -0.9396926. . .
• Cos 160° in radians: cos (8π/9) or cos (2.7925268 . . .)

What is the Value of Cos 160 Degrees?

The value of cos 160 degrees in decimal is -0.939692620. . .. Cos 160 degrees can also be expressed using the equivalent of the given angle (160 degrees) in radians (2.79252 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 160 degrees = 160° × (π/180°) rad = 8π/9 or 2.7925 . . .
∴ cos 160° = cos(2.7925) = -0.9396926. . .

Explanation:

For cos 160 degrees, the angle 160° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 160° value = -0.9396926. . .
Since the cosine function is a periodic function, we can represent cos 160° as, cos 160 degrees = cos(160° + n × 360°), n ∈ Z.
⇒ cos 160° = cos 520° = cos 880°, and so on.
Note: Since, cosine is an even function, the value of cos(-160°) = cos(160°).

Methods to Find Value of Cos 160 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 160° is given as -0.93969. . .. We can find the value of cos 160 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 160° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 160 degrees as:

• ± √(1-sin²(160°))
• ± 1/√(1 + tan²(160°))
• ± cot 160°/√(1 + cot²(160°))
• ±√(cosec²(160°) - 1)/cosec 160°
• 1/sec 160°

Note: Since 160° lies in the 2nd Quadrant, the final value of cos 160° will be negative.

We can use trigonometric identities to represent cos 160° as,

• -cos(180° - 160°) = -cos 20°
• -cos(180° + 160°) = -cos 340°
• sin(90° + 160°) = sin 250°
• sin(90° - 160°) = sin(-70°)

Cos 160 Degrees Using Unit Circle

To find the value of cos 160 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 160° angle with the positive x-axis.
• The cos of 160 degrees equals the x-coordinate(-0.9397) of the point of intersection (-0.9397, 0.342) of unit circle and r.

Hence the value of cos 160° = x = -0.9397 (approx)

☛ Also Check:

• cos 53 degrees
• cos 210 degrees
• cos 270 degrees
• cos 6 degrees
• cos 71 degrees
• cos 48 degrees

FAQs on Cos 160 Degrees

What is Cos 160 Degrees?

Cos 160 degrees is the value of cosine trigonometric function for an angle equal to 160 degrees. The value of cos 160° is -0.9397 (approx)

What is the Value of Cos 160° in Terms of Cosec 160°?

Since the cosine function can be represented using the cosecant function, we can write cos 160° as -[√(cosec²(160°) - 1)/cosec 160°]. The value of cosec 160° is equal to 2.92380.

What is the Value of Cos 160 Degrees in Terms of Sin 160°?

Using trigonometric identities, we can write cos 160° in terms of sin 160° as, cos(160°) = -√(1 - sin²(160°)). Here, the value of sin 160° is equal to 0.342.

How to Find Cos 160° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 160° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(160°))
• ± 1/√(1 + tan²(160°))
• ± cot 160°/√(1 + cot²(160°))
• ± √(cosec²(160°) - 1)/cosec 160°
• 1/sec 160°

☛ Also check: trigonometry table

How to Find the Value of Cos 160 Degrees?

The value of cos 160 degrees can be calculated by constructing an angle of 160° with the x-axis, and then finding the coordinates of the corresponding point (-0.9397, 0.342) on the unit circle. The value of cos 160° is equal to the x-coordinate (-0.9397). ∴ cos 160° = -0.9397.