Cos 61 Degrees

The value of cos 61 degrees is 0.4848096. . .. Cos 61 degrees in radians is written as cos (61° × π/180°), i.e., cos (1.064650. . .). In this article, we will discuss the methods to find the value of cos 61 degrees with examples.

• Cos 61°: 0.4848096. . .
• Cos (-61 degrees): 0.4848096. . .
• Cos 61° in radians: cos (1.0646508 . . .)

What is the Value of Cos 61 Degrees?

The value of cos 61 degrees in decimal is 0.484809620. . .. Cos 61 degrees can also be expressed using the equivalent of the given angle (61 degrees) in radians (1.06465 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 61 degrees = 61° × (π/180°) rad = 1.0646 . . .
∴ cos 61° = cos(1.0646) = 0.4848096. . .

Explanation:

For cos 61 degrees, the angle 61° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 61° value = 0.4848096. . .
Since the cosine function is a periodic function, we can represent cos 61° as, cos 61 degrees = cos(61° + n × 360°), n ∈ Z.
⇒ cos 61° = cos 421° = cos 781°, and so on.
Note: Since, cosine is an even function, the value of cos(-61°) = cos(61°).

Methods to Find Value of Cos 61 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 61° is given as 0.48480. . .. We can find the value of cos 61 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 61 Degrees Using Unit Circle

To find the value of cos 61 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 61° angle with the positive x-axis.
• The cos of 61 degrees equals the x-coordinate(0.4848) of the point of intersection (0.4848, 0.8746) of unit circle and r.

Hence the value of cos 61° = x = 0.4848 (approx)

Cos 61° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 61 degrees as:

• ± √(1-sin²(61°))
• ± 1/√(1 + tan²(61°))
• ± cot 61°/√(1 + cot²(61°))
• ±√(cosec²(61°) - 1)/cosec 61°
• 1/sec 61°

Note: Since 61° lies in the 1st Quadrant, the final value of cos 61° will be positive.

We can use trigonometric identities to represent cos 61° as,

• -cos(180° - 61°) = -cos 119°
• -cos(180° + 61°) = -cos 241°
• sin(90° + 61°) = sin 151°
• sin(90° - 61°) = sin 29°

☛ Also Check:

• cos 1 degrees
• cos 150 degrees
• cos 36 degrees
• cos 81 degrees
• cos 106 degrees
• cos 32 degrees

FAQs on Cos 61 Degrees

What is Cos 61 Degrees?

Cos 61 degrees is the value of cosine trigonometric function for an angle equal to 61 degrees. The value of cos 61° is 0.4848 (approx)

How to Find Cos 61° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 61° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(61°))
• ± 1/√(1 + tan²(61°))
• ± cot 61°/√(1 + cot²(61°))
• ± √(cosec²(61°) - 1)/cosec 61°
• 1/sec 61°

☛ Also check: trigonometry table

How to Find the Value of Cos 61 Degrees?

The value of cos 61 degrees can be calculated by constructing an angle of 61° with the x-axis, and then finding the coordinates of the corresponding point (0.4848, 0.8746) on the unit circle. The value of cos 61° is equal to the x-coordinate (0.4848). ∴ cos 61° = 0.4848.

What is the Value of Cos 61 Degrees in Terms of Tan 61°?

We know, using trig identities, we can write cos 61° as 1/√(1 + tan²(61°)). Here, the value of tan 61° is equal to 1.804047.

What is the Value of Cos 61° in Terms of Cosec 61°?

Since the cosine function can be represented using the cosecant function, we can write cos 61° as [√(cosec²(61°) - 1)/cosec 61°]. The value of cosec 61° is equal to 1.14335.