Cos 540 Degrees

The value of cos 540 degrees is -1. Cos 540 degrees in radians is written as cos (540° × π/180°), i.e., cos (3π) or cos (9.424777. . .). In this article, we will discuss the methods to find the value of cos 540 degrees with examples.

• Cos 540°: -1
• Cos (-540 degrees): -1
• Cos 540° in radians: cos (3π) or cos (9.4247779 . . .)

What is the Value of Cos 540 Degrees?

The value of cos 540 degrees is -1. Cos 540 degrees can also be expressed using the equivalent of the given angle (540 degrees) in radians (9.42477 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 540 degrees = 540° × (π/180°) rad = 3π or 9.4247 . . .
∴ cos 540° = cos(9.4247) = -1

Explanation:

For cos 540°, the angle 540° > 360°. Given the periodic property of the cosine function, we can represent it as cos(540° mod 360°) = cos(180°). The angle 540°, coterminal to angle 180°, lies on the negative x-axis.
Thus cos 540 degrees value = -1
Similarly, cos 540° can also be written as, cos 540 degrees = (540° + n × 360°), n ∈ Z.
⇒ cos 540° = cos 900° = cos 1260°, and so on.
Note: Since, cosine is an even function, the value of cos(-540°) = cos(540°).

Methods to Find Value of Cos 540 Degrees

The value of cos 540° is given as -1. We can find the value of cos 540 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 540° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 540 degrees as:

• ± √(1-sin²(540°))
• ± 1/√(1 + tan²(540°))
• ± cot 540°/√(1 + cot²(540°))
• ±√(cosec²(540°) - 1)/cosec 540°
• 1/sec 540°

Note: Since 540° lies on the negative x-axis, the final value of cos 540° is -1.

We can use trigonometric identities to represent cos 540° as,

• -cos(180° - 540°) = -cos(-360°)
• -cos(180° + 540°) = -cos 720°
• sin(90° + 540°) = sin 630°
• sin(90° - 540°) = sin(-450°)

Cos 540 Degrees Using Unit Circle

To find the value of cos 540 degrees using the unit circle, represent 540° in the form (1 × 360°) + 180° [∵ 540°>360°] ∵ cosine is a periodic function, cos 540° = cos 180°.

• Rotate ‘r’ anticlockwise to form 180° or 540° angle with the positive x-axis.
• The cos of 540 degrees equals the x-coordinate(-1) of the point of intersection (-1, 0) of unit circle and r.

Hence the value of cos 540° = x = -1

☛ Also Check:

• cos 2 degrees
• cos 37 degrees
• cos 3 degrees
• cos 280 degrees
• cos 25 degrees
• cos 70 degrees

FAQs on Cos 540 Degrees

What is Cos 540 Degrees?

Cos 540 degrees is the value of cosine trigonometric function for an angle equal to 540 degrees. The value of cos 540° is -1

How to Find Cos 540° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 540° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(540°))
• ± 1/√(1 + tan²(540°))
• ± cot 540°/√(1 + cot²(540°))
• ± √(cosec²(540°) - 1)/cosec 540°
• 1/sec 540°

☛ Also check: trigonometric table

How to Find the Value of Cos 540 Degrees?

The value of cos 540 degrees can be calculated by constructing an angle of 540° with the x-axis, and then finding the coordinates of the corresponding point (-1, 0) on the unit circle. The value of cos 540° is equal to the x-coordinate (-1). ∴ cos 540° = -1.

What is the Value of Cos 540 Degrees in Terms of Sin 540°?

Using trigonometric identities, we can write cos 540° in terms of sin 540° as, cos(540°) = -√(1 - sin²(540°)). Here, the value of sin 540° is equal to 0.

What is the Exact Value of cos 540 Degrees?

The exact value of cos 540 degrees is -1.