Cos 50 Degrees

The value of cos 50 degrees is 0.6427876. . .. Cos 50 degrees in radians is written as cos (50° × π/180°), i.e., cos (5π/18) or cos (0.872664. . .). In this article, we will discuss the methods to find the value of cos 50 degrees with examples.

• Cos 50°: 0.6427876. . .
• Cos (-50 degrees): 0.6427876. . .
• Cos 50° in radians: cos (5π/18) or cos (0.8726646 . . .)

What is the Value of Cos 50 Degrees?

The value of cos 50 degrees in decimal is 0.642787609. . .. Cos 50 degrees can also be expressed using the equivalent of the given angle (50 degrees) in radians (0.87266 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 50 degrees = 50° × (π/180°) rad = 5π/18 or 0.8726 . . .
∴ cos 50° = cos(0.8726) = 0.6427876. . .

Explanation:

For cos 50 degrees, the angle 50° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 50° value = 0.6427876. . .
Since the cosine function is a periodic function, we can represent cos 50° as, cos 50 degrees = cos(50° + n × 360°), n ∈ Z.
⇒ cos 50° = cos 410° = cos 770°, and so on.
Note: Since, cosine is an even function, the value of cos(-50°) = cos(50°).

Methods to Find Value of Cos 50 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 50° is given as 0.64278. . .. We can find the value of cos 50 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 50° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 50 degrees as:

• ± √(1-sin²(50°))
• ± 1/√(1 + tan²(50°))
• ± cot 50°/√(1 + cot²(50°))
• ±√(cosec²(50°) - 1)/cosec 50°
• 1/sec 50°

Note: Since 50° lies in the 1st Quadrant, the final value of cos 50° will be positive.

We can use trigonometric identities to represent cos 50° as,

• -cos(180° - 50°) = -cos 130°
• -cos(180° + 50°) = -cos 230°
• sin(90° + 50°) = sin 140°
• sin(90° - 50°) = sin 40°

Cos 50 Degrees Using Unit Circle

To find the value of cos 50 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 50° angle with the positive x-axis.
• The cos of 50 degrees equals the x-coordinate(0.6428) of the point of intersection (0.6428, 0.766) of unit circle and r.

Hence the value of cos 50° = x = 0.6428 (approx)

☛ Also Check:

• cos 240 degrees
• cos 270 degrees
• cos 11 degrees
• cos 89 degrees
• cos 44 degrees
• cos 34 degrees

FAQs on Cos 50 Degrees

What is Cos 50 Degrees?

Cos 50 degrees is the value of cosine trigonometric function for an angle equal to 50 degrees. The value of cos 50° is 0.6428 (approx)

What is the Value of Cos 50° in Terms of Cosec 50°?

Since the cosine function can be represented using the cosecant function, we can write cos 50° as [√(cosec²(50°) - 1)/cosec 50°]. The value of cosec 50° is equal to 1.30540.

How to Find Cos 50° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 50° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(50°))
• ± 1/√(1 + tan²(50°))
• ± cot 50°/√(1 + cot²(50°))
• ± √(cosec²(50°) - 1)/cosec 50°
• 1/sec 50°

☛ Also check: trigonometry table

What is the Value of Cos 50 Degrees in Terms of Sin 50°?

Using trigonometric identities, we can write cos 50° in terms of sin 50° as, cos(50°) = √(1 - sin²(50°)). Here, the value of sin 50° is equal to 0.766.

How to Find the Value of Cos 50 Degrees?

The value of cos 50 degrees can be calculated by constructing an angle of 50° with the x-axis, and then finding the coordinates of the corresponding point (0.6428, 0.766) on the unit circle. The value of cos 50° is equal to the x-coordinate (0.6428). ∴ cos 50° = 0.6428.