Cos 900 Degrees

The value of cos 900 degrees is -1. Cos 900 degrees in radians is written as cos (900° × π/180°), i.e., cos (5π) or cos (15.707963. . .). In this article, we will discuss the methods to find the value of cos 900 degrees with examples.

• Cos 900°: -1
• Cos (-900 degrees): -1
• Cos 900° in radians: cos (5π) or cos (15.7079632 . . .)

What is the Value of Cos 900 Degrees?

The value of cos 900 degrees is -1. Cos 900 degrees can also be expressed using the equivalent of the given angle (900 degrees) in radians (15.70796 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 900 degrees = 900° × (π/180°) rad = 5π or 15.7079 . . .
∴ cos 900° = cos(15.7079) = -1

Explanation:

For cos 900°, the angle 900° > 360°. Given the periodic property of the cosine function, we can represent it as cos(900° mod 360°) = cos(180°). The angle 900°, coterminal to angle 180°, lies on the negative x-axis.
Thus cos 900 degrees value = -1
Similarly, cos 900° can also be written as, cos 900 degrees = (900° + n × 360°), n ∈ Z.
⇒ cos 900° = cos 1260° = cos 1620°, and so on.
Note: Since, cosine is an even function, the value of cos(-900°) = cos(900°).

Methods to Find Value of Cos 900 Degrees

The value of cos 900° is given as -1. We can find the value of cos 900 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 900° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 900 degrees as:

• ± √(1-sin²(900°))
• ± 1/√(1 + tan²(900°))
• ± cot 900°/√(1 + cot²(900°))
• ±√(cosec²(900°) - 1)/cosec 900°
• 1/sec 900°

Note: Since 900° lies on the negative x-axis, the final value of cos 900° will be negative.

We can use trigonometric identities to represent cos 900° as,

• -cos(180° - 900°) = -cos(-720°)
• -cos(180° + 900°) = -cos 1080°
• sin(90° + 900°) = sin 990°
• sin(90° - 900°) = sin(-810°)

Cos 900 Degrees Using Unit Circle

To find the value of cos 900 degrees using the unit circle, represent 900° in the form (2 × 360°) + 180° [∵ 900°>360°] ∵ cosine is a periodic function, cos 900° = cos 180°.

• Rotate ‘r’ anticlockwise to form 180° or 900° angle with the positive x-axis.
• The cos of 900 degrees equals the x-coordinate(-1) of the point of intersection (-1, 0) of unit circle and r.

Hence the value of cos 900° = x = -1

☛ Also Check:

• cos 75 degrees
• cos 45 degrees
• cos 30 degrees
• cos 62 degrees
• cos 74 degrees
• cos 79 degrees

FAQs on Cos 900 Degrees

What is Cos 900 Degrees?

Cos 900 degrees is the value of cosine trigonometric function for an angle equal to 900 degrees. The value of cos 900° is -1.

What is the Value of Cos 900 Degrees in Terms of Cot 900°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 900° can be written as -cot 900°/√(1 + cot²(900°)).

How to Find Cos 900° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 900° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(900°))
• ± 1/√(1 + tan²(900°))
• ± cot 900°/√(1 + cot²(900°))
• ± √(cosec²(900°) - 1)/cosec 900°
• 1/sec 900°

☛ Also check: trigonometry table

How to Find the Value of Cos 900 Degrees?

The value of cos 900 degrees can be calculated by constructing an angle of 900° with the x-axis, and then finding the coordinates of the corresponding point (-1, 0) on the unit circle. The value of cos 900° is equal to the x-coordinate (-1). ∴ cos 900° = -1.

What is the Value of Cos 900° in Terms of Sec 900°?

Since the secant function is the reciprocal of the cosine function, we can write cos 900° as 1/sec(900°). The value of sec 900° is equal to -1.