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Cos 0 Degrees

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.

Cos 0°: 1
Cos (-0 degrees): 1
Cos 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 to 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 = 1
Since 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°, and so on.
Note: Since, cosine is an even function, the value of cos(-0°) = cos(0°).

Methods to 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 Functions
Using 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.

We can use trigonometric identities to 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 and r.

Hence the value of cos 0° = x = 1

☛ Also Check:

Examples Using Cos 0 Degrees

Example 1: Using the value of cos 0°, solve: (1-sin²(0°)).

Solution:
We know, (1-sin²(0°)) = (cos²(0°)) = 1
⇒ (1-sin²(0°)) = 1
Example 2: Find the value of cos 0° if sec 0° is 1.

Solution:
Since, cos 0° = 1/sec 0°
⇒ cos 0° = 1/1 = 1
Example 3: Find the value of 2 cos(0°)/3 sin(90°).

Solution:

Using trigonometric identities, we know, cos(0°) = sin(90° - 0°) = sin 90°.
⇒ cos(0°) = sin(90°)
⇒ Value of 2 cos(0°)/3 sin(90°) = 2/3

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FAQs on Cos 0 Degrees

What is Cos 0 Degrees?

Cos 0 degrees is the value of cosine trigonometric function for an angle equal to 0 degrees. The value of cos 0° is 1

What is the Value of Cos 0 Degrees in Terms of Tan 0°?

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

How to Find the Value of Cos 0 Degrees?

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

How to Find Cos 0° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 0° can be given in terms of other trigonometric functions as:

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

☛ Also check: trigonometry table

What is the Value of Cos 0° in Terms of Sec 0°?

Since the secant function is the reciprocal of the cosine function, we can write cos 0° as 1/sec(0°). The value of sec 0° is equal to 1.

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