The value of cos 0 degrees is 1. Cos 0 degrees in radians is written as cos (0° × π/180°), i.e., cos (0π) or cos (0). In this article, we will discuss the methods to find the value of cos 0 degrees with examples.

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Cos 0°: 1Cos (-0 degrees): 1Cos 0° in radians: cos (0π) or cos (0 . . .)

What is the Value of Cos 0 Degrees?

The value of cos 0 degrees is 1. Cos 0 degrees can also be expressed using the equivalent of the given angle (0 degrees) in radians (0 . . .)

We know, using degree lớn radian conversion, θ in radians = θ in degrees × (pi/180°)⇒ 0 degrees = 0° × (π/180°) rad = 0π or 0 . . .∴ cos 0° = cos(0) = 1

Explanation:

For cos 0 degrees, the angle 0° lies on the positive x-axis. Thus, cos 0° value = 1Since the cosine function is a periodic function, we can represent cos 0° as, cos 0 degrees = cos(0° + n × 360°), n ∈ Z.⇒ cos 0° = cos 360° = cos 720°, và so on.Note: Since, cosine is an even function, the value of cos(-0°) = cos(0°).

Methods lớn Find Value of Cos 0 Degrees

The value of cos 0° is given as 1. We can find the value of cos 0 degrees by:

Using Trigonometric FunctionsUsing Unit Circle

Cos 0° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 0 degrees as:

± √(1-sin²(0°))± 1/√(1 + tan²(0°))± cot 0°/√(1 + cot²(0°))±√(cosec²(0°) - 1)/cosec 0°1/sec 0°

Note: Since 0° lies on the positive x-axis, the final value of cos 0° will be positive.

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We can use trigonometric identities khổng lồ represent cos 0° as,

-cos(180° - 0°) = -cos 180°-cos(180° + 0°) = -cos 180°sin(90° + 0°) = sin 90°sin(90° - 0°) = sin 90°

Cos 0 Degrees Using Unit Circle

To find the value of cos 0 degrees using the unit circle:

Draw the radius of the unit circle,‘r’, to form 0° angle with the positive x-axis.The cos of 0 degrees equals the x-coordinate(1) of the point of intersection (1, 0) of unit circle và r.

Hence the value of cos 0° = x = 1