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Cos 270 Degrees

The value of cos 270 degrees is 0. Cos 270 degrees in radians is written as cos (270° × π/180°), i.e., cos (3π/2) or cos (4.712388. . .). In this article, we will discuss the methods to find the value of cos 270 degrees with examples.

Cos 270°: 0
Cos (-270 degrees): 0
Cos 270° in radians: cos (3π/2) or cos (4.7123889 . . .)

What is the Value of Cos 270 Degrees?

The value of cos 270 degrees is 0. Cos 270 degrees can also be expressed using the equivalent of the given angle (270 degrees) in radians (4.71238 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 270 degrees = 270° × (π/180°) rad = 3π/2 or 4.7123 . . .
∴ cos 270° = cos(4.7123) = 0

Explanation:

For cos 270 degrees, the angle 270° lies on the negative y-axis. Thus cos 270° value = 0
Since the cosine function is a periodic function, we can represent cos 270° as, cos 270 degrees = cos(270° + n × 360°), n ∈ Z.
⇒ cos 270° = cos 630° = cos 990°, and so on.
Note: Since, cosine is an even function, the value of cos(-270°) = cos(270°) = 0.

Methods to Find Value of Cos 270 Degrees

The value of cos 270° is given as 0. We can find the value of cos 270 degrees by:

Using Trigonometric Functions
Using Unit Circle

Cos 270° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 270 degrees as:

± √(1-sin²(270°))
± 1/√(1 + tan²(270°))
± cot 270°/√(1 + cot²(270°))
±√(cosec²(270°) - 1)/cosec 270°
1/sec 270°

Note: Since 270° lies on the negative y-axis, the final value of cos 270° will be 0.

We can use trigonometric identities to represent cos 270° as,

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

Cos 270 Degrees Using Unit Circle

To find the value of cos 270 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 270° angle with the positive x-axis.
The cos of 270 degrees equals the x-coordinate(0) of the point of intersection (0, -1) of unit circle and r.

Hence the value of cos 270° = x = 0

☛ Also Check:

Examples Using Cos 270 Degrees

Example 1: Find the value of cos 270° + sin 270°.

Solution:
Since, cos 270° = 0 and sin 270° = -1
⇒ cos 270° + sin 270° = 0 - 1 = -1
Example 2: Simplify: 9 (cos 270°/sin 90°)

Solution:

We know cos 270° = 0 and sin 90° = 1
⇒ 9 cos 270°/sin 90° = 9(0)
= 0
Example 3: Find the value of 2 cos(270°)/3 cos(180°).

Solution:

Using trigonometric identities, we know, cos(270°) = 0 and cos(180°) = -1.
⇒ Value of 2 cos(270°)/3 cos(180°) = 0

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FAQs on Cos 270 Degrees

What is Cos 270 Degrees?

Cos 270 degrees is the value of cosine trigonometric function for an angle equal to 270 degrees. The value of cos 270° is 0.

How to Find Cos 270° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 270° can be given in terms of other trigonometric functions as:

± √(1-sin²(270°))
± 1/√(1 + tan²(270°))
± cot 270°/√(1 + cot²(270°))
± √(cosec²(270°) - 1)/cosec 270°
1/sec 270°

☛ Also check: trigonometry table

What is the Exact Value of cos 270 Degrees?

The exact value of cos 270 degrees is 0.

How to Find the Value of Cos 270 Degrees?

The value of cos 270 degrees can be calculated by constructing an angle of 270° with the x-axis, and then finding the coordinates of the corresponding point (0, -1) on the unit circle. The value of cos 270° is equal to the x-coordinate (0). ∴ cos 270° = 0.

What is the Value of Cos 270 Degrees in Terms of Tan 270°?

We know, using trig identities, we can write cos 270° as 1/√(1 + tan²(270°)).

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