Cos 360

In mathematics, the cosine of 360 degrees equals 1. This is because the cosine function repeats every 360 degrees. At 360 degrees, the corresponding point on the unit circle is the same as at 0 degrees, so the cosine value is 1.

Cos 360 value in radian

The value of cos(2pie radians) is 1, where 2pie radians is equivalent to 360 degrees. In general, the cosine function is periodic with a period of 2pie radians.

Step to find The Value of cos 360 in radian are-

radians = (degrees x pie) / 180

Plugging in 360 degrees,

we get:

radians = (360 x pie) / 180

radians = 2pie .

Therefore, the value of cos(360 degrees) in radians is cos(2pie), which is equal to 1.

Read: How to Find the value of Cos 0?

Identities of Cos 360

  • cos 360° = sin (90 + 360°) = sin 450°
  • cos 360° = sin (90° - 360°) = sin -270°
  • -cos 360° = cos (180° + 360°) = cos 540°
  • -cos 360° = cos (180° - 360°) = cos -180°

Also Read: Converse of Pythagoras Theorem

How to Find Cos 360 degrees ?

Cosine is a trigonometric function that takes an angle in radians and returns a value between -1 and 1, representing the ratio of the adjacent side to the hypotenuse in a right triangle. On the unit circle, which has a radius of 1, the cosine of an angle corresponds to the x-coordinate of the point at that angle.

Since the cosine function repeats every 360 degrees, cos(360) is equivalent to cos(0). Therefore, the value of cos(360) is 1, the same as cos(0).

Cos 360-theta

The value of cos(360-theta) is equal to cos theta. This is because the cosine function has a period of 360 degrees and cos(360-theta) is equivalent to cos(theta+360), which is the same as cos theta.
cos(360° – theta) = cos(4 × 90° – theta)
Here, 90° is multiplied by 4, i.e. an even number, so cos will not change in the result. Also, 360° – theta comes in the fourth quadrant, where cos is always positive. So, cos(360° – theta) = cos theta.

Also Read: Continuous Variable

Cos 360+theta

The value of cos(360° + theta) is equal to cos(theta). This is because the cosine function has a period of 360 degrees, so adding or subtracting 360 degrees from an angle does not change its cosine value.

cos(360° + theta) = cos(4 × 90° + theta)

Here, 90° is multiplied by 4, i.e. an even number, so cos will not change in the result. Also, 360° + theta comes in the fourth quadrant, where all trigonometric ratios are positive, and cos is also positive. So, cos(360° + theta) = cos theta. Therefore, the value of cos 360 + theta  is equal to cos theta.

Trigonometrical Table to represent cos 360°

Angle

Sin

Cos

Tan

360°

0°

1°

0°

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Frequently Asked Questions on Cos 360