Cos 450 Degrees

The value of cos 450 degrees is 0. Cos 450 degrees in radians is written as cos (450° × π/180°), i.e., cos (5π/2) or cos (7.853981. . .). In this article, we will discuss the methods to find the value of cos 450 degrees with examples.

• Cos 450°: 0
• Cos (-450 degrees): 0
• Cos 450° in radians: cos (5π/2) or cos (7.8539816 . . .)

What is the Value of Cos 450 Degrees?

The value of cos 450 degrees is 0. Cos 450 degrees can also be expressed using the equivalent of the given angle (450 degrees) in radians (7.85398 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 450 degrees = 450° × (π/180°) rad = 5π/2 or 7.8539 . . .
∴ cos 450° = cos(7.8539) = 0

Explanation:

For cos 450°, the angle 450° > 360°. Given the periodic property of the cosine function, we can represent it as cos(450° mod 360°) = cos(90°). The angle 450°, coterminal to angle 90°, lies on the positive y-axis.
Thus cos 450 degrees value = 0
Similarly, cos 450° can also be written as, cos 450 degrees = (450° + n × 360°), n ∈ Z.
⇒ cos 450° = cos 810° = cos 1170°, and so on.
Note: Since, cosine is an even function, the value of cos(-450°) = cos(450°) = 0.

Methods to Find Value of Cos 450 Degrees

The value of cos 450° is given as 0. We can find the value of cos 450 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 450 Degrees Using Unit Circle

To find the value of cos 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ cosine is a periodic function, cos 450° = cos 90°.

• Rotate ‘r’ anticlockwise to form 90° or 450° angle with the positive x-axis.
• The cos of 450 degrees equals the x-coordinate(0) of the point of intersection (0, 1) of unit circle and r.

Hence the value of cos 450° = x = 0

Cos 450° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 450 degrees as:

• ± √(1-sin²(450°))
• ± 1/√(1 + tan²(450°))
• ± cot 450°/√(1 + cot²(450°))
• ±√(cosec²(450°) - 1)/cosec 450°
• 1/sec 450°

Note: Since 450° lies on the positive y-axis, the final value of cos 450° is 0.

We can use trigonometric identities to represent cos 450° as,

• -cos(180° - 450°) = -cos(-270°)
• -cos(180° + 450°) = -cos 630°
• sin(90° + 450°) = sin 540°
• sin(90° - 450°) = sin(-360°)

☛ Also Check:

• cos 18 degrees
• cos 300 degrees
• cos 270 degrees
• cos 115 degrees
• cos 42 degrees
• cos 79 degrees

FAQs on Cos 450 Degrees

What is Cos 450 Degrees?

Cos 450 degrees is the value of cosine trigonometric function for an angle equal to 450 degrees. The value of cos 450° is 0.

What is the Value of Cos 450 Degrees in Terms of Cot 450°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 450° can be written as cot 450°/√(1 + cot²(450°)). Here, the value of cot 450° is equal to 0.

What is the Exact Value of cos 450 Degrees?

The exact value of cos 450 degrees is 0.

How to Find the Value of Cos 450 Degrees?

The value of cos 450 degrees can be calculated by constructing an angle of 450° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of cos 450° is equal to the x-coordinate (0). ∴ cos 450° = 0.

How to Find Cos 450° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 450° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(450°))
• ± 1/√(1 + tan²(450°))
• ± cot 450°/√(1 + cot²(450°))
• ± √(cosec²(450°) - 1)/cosec 450°
• 1/sec 450°

☛ Also check: trigonometry table