Cos 78 Degrees

The value of cos 78 degrees is 0.2079116. . .. Cos 78 degrees in radians is written as cos (78° × π/180°), i.e., cos (13π/30) or cos (1.361356. . .). In this article, we will discuss the methods to find the value of cos 78 degrees with examples.

• Cos 78°: 0.2079116. . .
• Cos (-78 degrees): 0.2079116. . .
• Cos 78° in radians: cos (13π/30) or cos (1.3613568 . . .)

What is the Value of Cos 78 Degrees?

The value of cos 78 degrees in decimal is 0.207911690. . .. Cos 78 degrees can also be expressed using the equivalent of the given angle (78 degrees) in radians (1.36135 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 78 degrees = 78° × (π/180°) rad = 13π/30 or 1.3613 . . .
∴ cos 78° = cos(1.3613) = 0.2079116. . .

Explanation:

For cos 78 degrees, the angle 78° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 78° value = 0.2079116. . .
Since the cosine function is a periodic function, we can represent cos 78° as, cos 78 degrees = cos(78° + n × 360°), n ∈ Z.
⇒ cos 78° = cos 438° = cos 798°, and so on.
Note: Since, cosine is an even function, the value of cos(-78°) = cos(78°).

Methods to Find Value of Cos 78 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 78° is given as 0.20791. . .. We can find the value of cos 78 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 78 Degrees Using Unit Circle

To find the value of cos 78 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 78° angle with the positive x-axis.
• The cos of 78 degrees equals the x-coordinate(0.2079) of the point of intersection (0.2079, 0.9781) of unit circle and r.

Hence the value of cos 78° = x = 0.2079 (approx)

Cos 78° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 78 degrees as:

• ± √(1-sin²(78°))
• ± 1/√(1 + tan²(78°))
• ± cot 78°/√(1 + cot²(78°))
• ±√(cosec²(78°) - 1)/cosec 78°
• 1/sec 78°

Note: Since 78° lies in the 1st Quadrant, the final value of cos 78° will be positive.

We can use trigonometric identities to represent cos 78° as,

• -cos(180° - 78°) = -cos 102°
• -cos(180° + 78°) = -cos 258°
• sin(90° + 78°) = sin 168°
• sin(90° - 78°) = sin 12°

☛ Also Check:

• cos 30 degrees
• cos 18 degrees
• cos 2 degrees
• cos 65 degrees
• cos 5 degrees
• cos 48 degrees

FAQs on Cos 78 Degrees

What is Cos 78 Degrees?

Cos 78 degrees is the value of cosine trigonometric function for an angle equal to 78 degrees. The value of cos 78° is 0.2079 (approx)

What is the Value of Cos 78 Degrees in Terms of Cot 78°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 78° can be written as cot 78°/√(1 + cot²(78°)). Here, the value of cot 78° is equal to 0.21255.

What is the Value of Cos 78° in Terms of Sec 78°?

Since the secant function is the reciprocal of the cosine function, we can write cos 78° as 1/sec(78°). The value of sec 78° is equal to 4.809734.

How to Find Cos 78° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 78° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(78°))
• ± 1/√(1 + tan²(78°))
• ± cot 78°/√(1 + cot²(78°))
• ± √(cosec²(78°) - 1)/cosec 78°
• 1/sec 78°

☛ Also check: trigonometric table

How to Find the Value of Cos 78 Degrees?

The value of cos 78 degrees can be calculated by constructing an angle of 78° with the x-axis, and then finding the coordinates of the corresponding point (0.2079, 0.9781) on the unit circle. The value of cos 78° is equal to the x-coordinate (0.2079). ∴ cos 78° = 0.2079.