Cos 780 Degrees

The value of cos 780 degrees is 0.5. Cos 780 degrees in radians is written as cos (780° × π/180°), i.e., cos (13π/3) or cos (13.613568. . .). In this article, we will discuss the methods to find the value of cos 780 degrees with examples.

• Cos 780°: 0.5
• Cos 780° in fraction: 1/2
• Cos (-780 degrees): 0.5
• Cos 780° in radians: cos (13π/3) or cos (13.6135681 . . .)

What is the Value of Cos 780 Degrees?

The value of cos 780 degrees in decimal is 0.5. Cos 780 degrees can also be expressed using the equivalent of the given angle (780 degrees) in radians (13.61356 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 780 degrees = 780° × (π/180°) rad = 13π/3 or 13.6135 . . .
∴ cos 780° = cos(13.6135) = 1/2 or 0.5

Explanation:

For cos 780°, the angle 780° > 360°. Given the periodic property of the cosine function, we can represent it as cos(780° mod 360°) = cos(60°). The angle 780°, coterminal to angle 60°, is located in the First Quadrant(Quadrant I).
Since cosine function is positive in the 1st quadrant, thus cos 780 degrees value = 1/2 or 0.5
Similarly, cos 780° can also be written as, cos 780 degrees = (780° + n × 360°), n ∈ Z.
⇒ cos 780° = cos 1140° = cos 1500°, and so on.
Note: Since, cosine is an even function, the value of cos(-780°) = cos(780°).

Methods to Find Value of Cos 780 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 780° is given as 0.5. We can find the value of cos 780 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 780° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 780 degrees as:

• ± √(1-sin²(780°))
• ± 1/√(1 + tan²(780°))
• ± cot 780°/√(1 + cot²(780°))
• ±√(cosec²(780°) - 1)/cosec 780°
• 1/sec 780°

Note: Since 780° lies in the 1st Quadrant, the final value of cos 780° will be positive.

We can use trigonometric identities to represent cos 780° as,

• -cos(180° - 780°) = -cos(-600°)
• -cos(180° + 780°) = -cos 960°
• sin(90° + 780°) = sin 870°
• sin(90° - 780°) = sin(-690°)

Cos 780 Degrees Using Unit Circle

To find the value of cos 780 degrees using the unit circle, represent 780° in the form (2 × 360°) + 60° [∵ 780°>360°] ∵ cosine is a periodic function, cos 780° = cos 60°.

• Rotate ‘r’ anticlockwise to form 60° or 780° angle with the positive x-axis.
• The cos of 780 degrees equals the x-coordinate(0.5) of the point of intersection (0.5, 0.866) of unit circle and r.

Hence the value of cos 780° = x = 0.5

☛ Also Check:

• cos 15 degrees
• cos 300 degrees
• cos 1 degrees
• cos 125 degrees
• cos 630 degrees
• cos 19 degrees

FAQs on Cos 780 Degrees

What is Cos 780 Degrees?

Cos 780 degrees is the value of cosine trigonometric function for an angle equal to 780 degrees. The value of cos 780° is 1/2 or 0.5

How to Find Cos 780° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 780° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(780°))
• ± 1/√(1 + tan²(780°))
• ± cot 780°/√(1 + cot²(780°))
• ± √(cosec²(780°) - 1)/cosec 780°
• 1/sec 780°

☛ Also check: trigonometric table

How to Find the Value of Cos 780 Degrees?

The value of cos 780 degrees can be calculated by constructing an angle of 780° with the x-axis, and then finding the coordinates of the corresponding point (0.5, 0.866) on the unit circle. The value of cos 780° is equal to the x-coordinate (0.5). ∴ cos 780° = 0.5.

What is the Value of Cos 780 Degrees in Terms of Sin 780°?

Using trigonometric identities, we can write cos 780° in terms of sin 780° as, cos(780°) = √(1 - sin²(780°)). Here, the value of sin 780° is equal to 0.866.

What is the Exact Value of cos 780 Degrees?

The exact value of cos 780 degrees is 0.5.