Cos 83 Degrees

The value of cos 83 degrees is 0.1218693. . .. Cos 83 degrees in radians is written as cos (83° × π/180°), i.e., cos (1.448623. . .). In this article, we will discuss the methods to find the value of cos 83 degrees with examples.

• Cos 83°: 0.1218693. . .
• Cos (-83 degrees): 0.1218693. . .
• Cos 83° in radians: cos (1.4486232 . . .)

What is the Value of Cos 83 Degrees?

The value of cos 83 degrees in decimal is 0.121869343. . .. Cos 83 degrees can also be expressed using the equivalent of the given angle (83 degrees) in radians (1.44862 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 83 degrees = 83° × (π/180°) rad = 1.4486 . . .
∴ cos 83° = cos(1.4486) = 0.1218693. . .

Explanation:

For cos 83 degrees, the angle 83° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 83° value = 0.1218693. . .
Since the cosine function is a periodic function, we can represent cos 83° as, cos 83 degrees = cos(83° + n × 360°), n ∈ Z.
⇒ cos 83° = cos 443° = cos 803°, and so on.
Note: Since, cosine is an even function, the value of cos(-83°) = cos(83°).

Methods to Find Value of Cos 83 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 83° is given as 0.12186. . .. We can find the value of cos 83 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 83 Degrees Using Unit Circle

To find the value of cos 83 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 83° angle with the positive x-axis.
• The cos of 83 degrees equals the x-coordinate(0.1219) of the point of intersection (0.1219, 0.9925) of unit circle and r.

Hence the value of cos 83° = x = 0.1219 (approx)

Cos 83° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 83 degrees as:

• ± √(1-sin²(83°))
• ± 1/√(1 + tan²(83°))
• ± cot 83°/√(1 + cot²(83°))
• ±√(cosec²(83°) - 1)/cosec 83°
• 1/sec 83°

Note: Since 83° lies in the 1st Quadrant, the final value of cos 83° will be positive.

We can use trigonometric identities to represent cos 83° as,

• -cos(180° - 83°) = -cos 97°
• -cos(180° + 83°) = -cos 263°
• sin(90° + 83°) = sin 173°
• sin(90° - 83°) = sin 7°

☛ Also Check:

• cos 150 degrees
• cos 225 degrees
• cos 53 degrees
• cos 80 degrees
• cos 285 degrees
• cos 41 degrees

FAQs on Cos 83 Degrees

What is Cos 83 Degrees?

Cos 83 degrees is the value of cosine trigonometric function for an angle equal to 83 degrees. The value of cos 83° is 0.1219 (approx)

How to Find the Value of Cos 83 Degrees?

The value of cos 83 degrees can be calculated by constructing an angle of 83° with the x-axis, and then finding the coordinates of the corresponding point (0.1219, 0.9925) on the unit circle. The value of cos 83° is equal to the x-coordinate (0.1219). ∴ cos 83° = 0.1219.

What is the Value of Cos 83° in Terms of Sec 83°?

Since the secant function is the reciprocal of the cosine function, we can write cos 83° as 1/sec(83°). The value of sec 83° is equal to 8.205509.

What is the Value of Cos 83 Degrees in Terms of Sin 83°?

Using trigonometric identities, we can write cos 83° in terms of sin 83° as, cos(83°) = √(1 - sin²(83°)). Here, the value of sin 83° is equal to 0.9925.

How to Find Cos 83° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 83° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(83°))
• ± 1/√(1 + tan²(83°))
• ± cot 83°/√(1 + cot²(83°))
• ± √(cosec²(83°) - 1)/cosec 83°
• 1/sec 83°

☛ Also check: trigonometry table