Cos 340 Degrees

The value of cos 340 degrees is 0.9396926. . .. Cos 340 degrees in radians is written as cos (340° × π/180°), i.e., cos (17π/9) or cos (5.934119. . .). In this article, we will discuss the methods to find the value of cos 340 degrees with examples.

• Cos 340°: 0.9396926. . .
• Cos (-340 degrees): 0.9396926. . .
• Cos 340° in radians: cos (17π/9) or cos (5.9341194 . . .)

What is the Value of Cos 340 Degrees?

The value of cos 340 degrees in decimal is 0.939692620. . .. Cos 340 degrees can also be expressed using the equivalent of the given angle (340 degrees) in radians (5.93411 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 340 degrees = 340° × (π/180°) rad = 17π/9 or 5.9341 . . .
∴ cos 340° = cos(5.9341) = 0.9396926. . .

Explanation:

For cos 340 degrees, the angle 340° lies between 270° and 360° (Fourth Quadrant). Since cosine function is positive in the fourth quadrant, thus cos 340° value = 0.9396926. . .
Since the cosine function is a periodic function, we can represent cos 340° as, cos 340 degrees = cos(340° + n × 360°), n ∈ Z.
⇒ cos 340° = cos 700° = cos 1060°, and so on.
Note: Since, cosine is an even function, the value of cos(-340°) = cos(340°).

Methods to Find Value of Cos 340 Degrees

The cosine function is positive in the 4th quadrant. The value of cos 340° is given as 0.93969. . .. We can find the value of cos 340 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 340 Degrees Using Unit Circle

To find the value of cos 340 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 340° angle with the positive x-axis.
• The cos of 340 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 340° = x = 0.9397 (approx)

Cos 340° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 340 degrees as:

• ± √(1-sin²(340°))
• ± 1/√(1 + tan²(340°))
• ± cot 340°/√(1 + cot²(340°))
• ±√(cosec²(340°) - 1)/cosec 340°
• 1/sec 340°

Note: Since 340° lies in the 4th Quadrant, the final value of cos 340° will be positive.

We can use trigonometric identities to represent cos 340° as,

• -cos(180° - 340°) = -cos(-160°)
• -cos(180° + 340°) = -cos 520°
• sin(90° + 340°) = sin 430°
• sin(90° - 340°) = sin(-250°)

☛ Also Check:

• cos 360 degrees
• cos 240 degrees
• cos 2 degrees
• cos 1140 degrees
• cos 61 degrees
• cos 78 degrees

FAQs on Cos 340 Degrees

What is Cos 340 Degrees?

Cos 340 degrees is the value of cosine trigonometric function for an angle equal to 340 degrees. The value of cos 340° is 0.9397 (approx)

How to Find the Value of Cos 340 Degrees?

The value of cos 340 degrees can be calculated by constructing an angle of 340° 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 340° is equal to the x-coordinate (0.9397). ∴ cos 340° = 0.9397.

What is the Value of Cos 340° in Terms of Cosec 340°?

Since the cosine function can be represented using the cosecant function, we can write cos 340° as -[√(cosec²(340°) - 1)/cosec 340°]. The value of cosec 340° is equal to -2.92380.

How to Find Cos 340° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 340° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(340°))
• ± 1/√(1 + tan²(340°))
• ± cot 340°/√(1 + cot²(340°))
• ± √(cosec²(340°) - 1)/cosec 340°
• 1/sec 340°

☛ Also check: trigonometry table

What is the Value of Cos 340 Degrees in Terms of Tan 340°?

We know, using trig identities, we can write cos 340° as 1/√(1 + tan²(340°)). Here, the value of tan 340° is equal to -0.363970.