Cos 58 Degrees

The value of cos 58 degrees is 0.5299192. . .. Cos 58 degrees in radians is written as cos (58° × π/180°), i.e., cos (29π/90) or cos (1.012290. . .). In this article, we will discuss the methods to find the value of cos 58 degrees with examples.

• Cos 58°: 0.5299192. . .
• Cos (-58 degrees): 0.5299192. . .
• Cos 58° in radians: cos (29π/90) or cos (1.0122909 . . .)

What is the Value of Cos 58 Degrees?

The value of cos 58 degrees in decimal is 0.529919264. . .. Cos 58 degrees can also be expressed using the equivalent of the given angle (58 degrees) in radians (1.01229 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 58 degrees = 58° × (π/180°) rad = 29π/90 or 1.0122 . . .
∴ cos 58° = cos(1.0122) = 0.5299192. . .

Explanation:

For cos 58 degrees, the angle 58° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 58° value = 0.5299192. . .
Since the cosine function is a periodic function, we can represent cos 58° as, cos 58 degrees = cos(58° + n × 360°), n ∈ Z.
⇒ cos 58° = cos 418° = cos 778°, and so on.
Note: Since, cosine is an even function, the value of cos(-58°) = cos(58°).

Methods to Find Value of Cos 58 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 58° is given as 0.52991. . .. We can find the value of cos 58 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 58° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 58 degrees as:

• ± √(1-sin²(58°))
• ± 1/√(1 + tan²(58°))
• ± cot 58°/√(1 + cot²(58°))
• ±√(cosec²(58°) - 1)/cosec 58°
• 1/sec 58°

Note: Since 58° lies in the 1st Quadrant, the final value of cos 58° will be positive.

We can use trigonometric identities to represent cos 58° as,

• -cos(180° - 58°) = -cos 122°
• -cos(180° + 58°) = -cos 238°
• sin(90° + 58°) = sin 148°
• sin(90° - 58°) = sin 32°

Cos 58 Degrees Using Unit Circle

To find the value of cos 58 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 58° angle with the positive x-axis.
• The cos of 58 degrees equals the x-coordinate(0.5299) of the point of intersection (0.5299, 0.848) of unit circle and r.

Hence the value of cos 58° = x = 0.5299 (approx)

☛ Also Check:

• cos 21 degrees
• cos 20 degrees
• cos 150 degrees
• cos 320 degrees
• cos 660 degrees
• cos 74 degrees

FAQs on Cos 58 Degrees

What is Cos 58 Degrees?

Cos 58 degrees is the value of cosine trigonometric function for an angle equal to 58 degrees. The value of cos 58° is 0.5299 (approx)

How to Find the Value of Cos 58 Degrees?

The value of cos 58 degrees can be calculated by constructing an angle of 58° with the x-axis, and then finding the coordinates of the corresponding point (0.5299, 0.848) on the unit circle. The value of cos 58° is equal to the x-coordinate (0.5299). ∴ cos 58° = 0.5299.

How to Find Cos 58° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 58° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(58°))
• ± 1/√(1 + tan²(58°))
• ± cot 58°/√(1 + cot²(58°))
• ± √(cosec²(58°) - 1)/cosec 58°
• 1/sec 58°

☛ Also check: trigonometry table

What is the Value of Cos 58° in Terms of Sec 58°?

Since the secant function is the reciprocal of the cosine function, we can write cos 58° as 1/sec(58°). The value of sec 58° is equal to 1.887079.

What is the Value of Cos 58 Degrees in Terms of Cot 58°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 58° can be written as cot 58°/√(1 + cot²(58°)). Here, the value of cot 58° is equal to 0.62486.