Cos 59 Degrees

The value of cos 59 degrees is 0.5150380. . .. Cos 59 degrees in radians is written as cos (59° × π/180°), i.e., cos (1.029744. . .). In this article, we will discuss the methods to find the value of cos 59 degrees with examples.

• Cos 59°: 0.5150380. . .
• Cos (-59 degrees): 0.5150380. . .
• Cos 59° in radians: cos (1.0297442 . . .)

What is the Value of Cos 59 Degrees?

The value of cos 59 degrees in decimal is 0.515038074. . .. Cos 59 degrees can also be expressed using the equivalent of the given angle (59 degrees) in radians (1.02974 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 59 degrees = 59° × (π/180°) rad = 1.0297 . . .
∴ cos 59° = cos(1.0297) = 0.5150380. . .

Explanation:

For cos 59 degrees, the angle 59° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 59° value = 0.5150380. . .
Since the cosine function is a periodic function, we can represent cos 59° as, cos 59 degrees = cos(59° + n × 360°), n ∈ Z.
⇒ cos 59° = cos 419° = cos 779°, and so on.
Note: Since, cosine is an even function, the value of cos(-59°) = cos(59°).

Methods to Find Value of Cos 59 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 59° is given as 0.51503. . .. We can find the value of cos 59 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 59 Degrees Using Unit Circle

To find the value of cos 59 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 59° angle with the positive x-axis.
• The cos of 59 degrees equals the x-coordinate(0.515) of the point of intersection (0.515, 0.8572) of unit circle and r.

Hence the value of cos 59° = x = 0.515 (approx)

Cos 59° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 59 degrees as:

• ± √(1-sin²(59°))
• ± 1/√(1 + tan²(59°))
• ± cot 59°/√(1 + cot²(59°))
• ±√(cosec²(59°) - 1)/cosec 59°
• 1/sec 59°

Note: Since 59° lies in the 1st Quadrant, the final value of cos 59° will be positive.

We can use trigonometric identities to represent cos 59° as,

• -cos(180° - 59°) = -cos 121°
• -cos(180° + 59°) = -cos 239°
• sin(90° + 59°) = sin 149°
• sin(90° - 59°) = sin 31°

☛ Also Check:

• cos 135 degrees
• cos 18 degrees
• cos 2 degrees
• cos 6 degrees
• cos 1125 degrees
• cos 35 degrees

FAQs on Cos 59 Degrees

What is Cos 59 Degrees?

Cos 59 degrees is the value of cosine trigonometric function for an angle equal to 59 degrees. The value of cos 59° is 0.515 (approx)

What is the Value of Cos 59° in Terms of Cosec 59°?

Since the cosine function can be represented using the cosecant function, we can write cos 59° as [√(cosec²(59°) - 1)/cosec 59°]. The value of cosec 59° is equal to 1.16663.

How to Find Cos 59° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 59° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(59°))
• ± 1/√(1 + tan²(59°))
• ± cot 59°/√(1 + cot²(59°))
• ± √(cosec²(59°) - 1)/cosec 59°
• 1/sec 59°

☛ Also check: trigonometry table

What is the Value of Cos 59 Degrees in Terms of Sin 59°?

Using trigonometric identities, we can write cos 59° in terms of sin 59° as, cos(59°) = √(1 - sin²(59°)). Here, the value of sin 59° is equal to 0.8572.

How to Find the Value of Cos 59 Degrees?

The value of cos 59 degrees can be calculated by constructing an angle of 59° with the x-axis, and then finding the coordinates of the corresponding point (0.515, 0.8572) on the unit circle. The value of cos 59° is equal to the x-coordinate (0.515). ∴ cos 59° = 0.515.