Cos 720 Degrees

The value of cos 720 degrees is 1. Cos 720 degrees in radians is written as cos (720° × π/180°), i.e., cos (4π) or cos (12.566370. . .). In this article, we will discuss the methods to find the value of cos 720 degrees with examples.

• Cos 720°: 1
• Cos (-720 degrees): 1
• Cos 720° in radians: cos (4π) or cos (12.5663706 . . .)

What is the Value of Cos 720 Degrees?

The value of cos 720 degrees is 1. Cos 720 degrees can also be expressed using the equivalent of the given angle (720 degrees) in radians (12.56637 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 720 degrees = 720° × (π/180°) rad = 4π or 12.5663 . . .
∴ cos 720° = cos(12.5663) = 1

Explanation:

For cos 720°, the angle 720° > 360°. Given the periodic property of the cosine function, we can represent it as cos(720° mod 360°) = cos(0°). The angle 720°, coterminal to angle 0°, lies on the positive x-axis.
Thus cos 720 degrees value = 1
Similarly, cos 720° can also be written as, cos 720 degrees = (720° + n × 360°), n ∈ Z.
⇒ cos 720° = cos 1080° = cos 1440°, and so on.
Note: Since, cosine is an even function, the value of cos(-720°) = cos(720°).

Methods to Find Value of Cos 720 Degrees

The value of cos 720° is given as 1. We can find the value of cos 720 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 720° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 720 degrees as:

• ± √(1-sin²(720°))
• ± 1/√(1 + tan²(720°))
• ± cot 720°/√(1 + cot²(720°))
• ±√(cosec²(720°) - 1)/cosec 720°
• 1/sec 720°

Note: Since 720° lies on the positive x-axis, the final value of cos 720° will be positive.

We can use trigonometric identities to represent cos 720° as,

• -cos(180° - 720°) = -cos(-540°)
• -cos(180° + 720°) = -cos 900°
• sin(90° + 720°) = sin 810°
• sin(90° - 720°) = sin(-630°)

Cos 720 Degrees Using Unit Circle

To find the value of cos 720 degrees using the unit circle, represent 720° in the form (2 × 360°) + 0° [∵ 720°>360°] ∵ cosine is a periodic function, cos 720° = cos 0°.

• Rotate ‘r’ anticlockwise to form 0° or 720° angle with the positive x-axis.
• The cos of 720 degrees equals the x-coordinate(1) of the point of intersection (1, 0) of unit circle and r.

Hence the value of cos 720° = x = 1

☛ Also Check:

• cos 37 degrees
• cos 30 degrees
• cos 150 degrees
• cos 320 degrees
• cos 6 degrees
• cos 720 degrees

FAQs on Cos 720 Degrees

What is Cos 720 Degrees?

Cos 720 degrees is the value of cosine trigonometric function for an angle equal to 720 degrees. The value of cos 720° is 1.

What is the Value of Cos 720 Degrees in Terms of Tan 720°?

We know, using trig identities, we can write cos 720° as 1/√(1 + tan²(720°)). Here, the value of tan 720° is equal to 0.

What is the Value of Cos 720° in Terms of Sec 720°?

Since the secant function is the reciprocal of the cosine function, we can write cos 720° as 1/sec(720°). The value of sec 720° is equal to 1.

How to Find Cos 720° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 720° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(720°))
• ± 1/√(1 + tan²(720°))
• ± cot 720°/√(1 + cot²(720°))
• ± √(cosec²(720°) - 1)/cosec 720°
• 1/sec 720°

☛ Also check: trigonometric table

How to Find the Value of Cos 720 Degrees?

The value of cos 720 degrees can be calculated by constructing an angle of 720° with the x-axis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of cos 720° is equal to the x-coordinate (1). ∴ cos 720° = 1.