Cos 1170 Degrees

The value of cos 1170 degrees is 0. Cos 1170 degrees in radians is written as cos (1170° × π/180°), i.e., cos (13π/2) or cos (20.420352. . .). In this article, we will discuss the methods to find the value of cos 1170 degrees with examples.

• Cos 1170°: 0
• Cos (-1170 degrees): 0
• Cos 1170° in radians: cos (13π/2) or cos (20.4203522 . . .)

What is the Value of Cos 1170 Degrees?

The value of cos 1170 degrees is 0. Cos 1170 degrees can also be expressed using the equivalent of the given angle (1170 degrees) in radians (20.42035 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1170 degrees = 1170° × (π/180°) rad = 13π/2 or 20.4203 . . .
∴ cos 1170° = cos(20.4203) = 0

Explanation:

For cos 1170°, the angle 1170° > 360°. Given the periodic property of the cosine function, we can represent it as cos(1170° mod 360°) = cos(90°). The angle 1170°, coterminal to angle 90°, lies on the positive y-axis.
Thus cos 1170 degrees value = 0
Similarly, cos 1170° can also be written as, cos 1170 degrees = (1170° + n × 360°), n ∈ Z.
⇒ cos 1170° = cos 1530° = cos 1890°, and so on.
Note: Since, cosine is an even function, the value of cos(-1170°) = cos(1170°) = 0.

Methods to Find Value of Cos 1170 Degrees

The value of cos 1170° is given as 0. We can find the value of cos 1170 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 1170 Degrees Using Unit Circle

To find the value of cos 1170 degrees using the unit circle, represent 1170° in the form (3 × 360°) + 90° [∵ 1170°>360°] ∵ cosine is a periodic function, cos 1170° = cos 90°.

• Rotate ‘r’ anticlockwise to form 90° or 1170° angle with the positive x-axis.
• The cos of 1170 degrees equals the x-coordinate(0) of the point of intersection (0, 1) of unit circle and r.

Hence the value of cos 1170° = x = 0

Cos 1170° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 1170 degrees as:

• ± √(1-sin²(1170°))
• ± 1/√(1 + tan²(1170°))
• ± cot 1170°/√(1 + cot²(1170°))
• ±√(cosec²(1170°) - 1)/cosec 1170°
• 1/sec 1170°

Note: Since 1170° lies on the positive y-axis, the final value of cos 1170° is 0.

We can use trigonometric identities to represent cos 1170° as,

• -cos(180° - 1170°) = -cos(-990°)
• -cos(180° + 1170°) = -cos 1350°
• sin(90° + 1170°) = sin 1260°
• sin(90° - 1170°) = sin(-1080°)

☛ Also Check:

• cos 120 degrees
• cos 210 degrees
• cos 3 degrees
• cos 55 degrees
• cos 38 degrees
• cos 83 degrees

FAQs on Cos 1170 Degrees

What is Cos 1170 Degrees?

Cos 1170 degrees is the value of cosine trigonometric function for an angle equal to 1170 degrees. The value of cos 1170° is 0.

What is the Value of Cos 1170 Degrees in Terms of Tan 1170°?

We know, using trig identities, we can write cos 1170° as 1/√(1 + tan²(1170°)). 

How to Find the Value of Cos 1170 Degrees?

The value of cos 1170 degrees can be calculated by constructing an angle of 1170° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of cos 1170° is equal to the x-coordinate (0). ∴ cos 1170° = 0.

How to Find Cos 1170° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 1170° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(1170°))
• ± 1/√(1 + tan²(1170°))
• ± cot 1170°/√(1 + cot²(1170°))
• ± √(cosec²(1170°) - 1)/cosec 1170°
• 1/sec 1170°

☛ Also check: trigonometric table

What is the Value of Cos 1170° in Terms of Cosec 1170°?

Since the cosine function can be represented using the cosecant function, we can write cos 1170° as [√(cosec²(1170°) - 1)/cosec 1170°]. The value of cosec 1170° is equal to 1.