Cos 318 Degrees

The value of cos 318 degrees is 0.7431448. . .. Cos 318 degrees in radians is written as cos (318° × π/180°), i.e., cos (53π/30) or cos (5.550147. . .). In this article, we will discuss the methods to find the value of cos 318 degrees with examples.

• Cos 318°: 0.7431448. . .
• Cos (-318 degrees): 0.7431448. . .
• Cos 318° in radians: cos (53π/30) or cos (5.5501470 . . .)

What is the Value of Cos 318 Degrees?

The value of cos 318 degrees in decimal is 0.743144825. . .. Cos 318 degrees can also be expressed using the equivalent of the given angle (318 degrees) in radians (5.55014 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 318 degrees = 318° × (π/180°) rad = 53π/30 or 5.5501 . . .
∴ cos 318° = cos(5.5501) = 0.7431448. . .

Explanation:

For cos 318 degrees, the angle 318° lies between 270° and 360° (Fourth Quadrant). Since cosine function is positive in the fourth quadrant, thus cos 318° value = 0.7431448. . .
Since the cosine function is a periodic function, we can represent cos 318° as, cos 318 degrees = cos(318° + n × 360°), n ∈ Z.
⇒ cos 318° = cos 678° = cos 1038°, and so on.
Note: Since, cosine is an even function, the value of cos(-318°) = cos(318°).

Methods to Find Value of Cos 318 Degrees

The cosine function is positive in the 4th quadrant. The value of cos 318° is given as 0.74314. . .. We can find the value of cos 318 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 318 Degrees Using Unit Circle

To find the value of cos 318 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 318° angle with the positive x-axis.
• The cos of 318 degrees equals the x-coordinate(0.7431) of the point of intersection (0.7431, -0.6691) of unit circle and r.

Hence the value of cos 318° = x = 0.7431 (approx)

Cos 318° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 318 degrees as:

• ± √(1-sin²(318°))
• ± 1/√(1 + tan²(318°))
• ± cot 318°/√(1 + cot²(318°))
• ±√(cosec²(318°) - 1)/cosec 318°
• 1/sec 318°

Note: Since 318° lies in the 4th Quadrant, the final value of cos 318° will be positive.

We can use trigonometric identities to represent cos 318° as,

• -cos(180° - 318°) = -cos(-138°)
• -cos(180° + 318°) = -cos 498°
• sin(90° + 318°) = sin 408°
• sin(90° - 318°) = sin(-228°)

☛ Also Check:

• cos 18 degrees
• cos 20 degrees
• cos 75 degrees
• cos 450 degrees
• cos 42 degrees
• cos 43 degrees

FAQs on Cos 318 Degrees

What is Cos 318 Degrees?

Cos 318 degrees is the value of cosine trigonometric function for an angle equal to 318 degrees. The value of cos 318° is 0.7431 (approx)

How to Find the Value of Cos 318 Degrees?

The value of cos 318 degrees can be calculated by constructing an angle of 318° with the x-axis, and then finding the coordinates of the corresponding point (0.7431, -0.6691) on the unit circle. The value of cos 318° is equal to the x-coordinate (0.7431). ∴ cos 318° = 0.7431.

What is the Value of Cos 318° in Terms of Cosec 318°?

Since the cosine function can be represented using the cosecant function, we can write cos 318° as -[√(cosec²(318°) - 1)/cosec 318°]. The value of cosec 318° is equal to -1.49447.

How to Find Cos 318° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 318° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(318°))
• ± 1/√(1 + tan²(318°))
• ± cot 318°/√(1 + cot²(318°))
• ± √(cosec²(318°) - 1)/cosec 318°
• 1/sec 318°

☛ Also check: trigonometry table

What is the Value of Cos 318 Degrees in Terms of Cot 318°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 318° can be written as -cot 318°/√(1 + cot²(318°)). Here, the value of cot 318° is equal to -1.11061.