Cos 66 Degrees

The value of cos 66 degrees is 0.4067366. . .. Cos 66 degrees in radians is written as cos (66° × π/180°), i.e., cos (11π/30) or cos (1.151917. . .). In this article, we will discuss the methods to find the value of cos 66 degrees with examples.

• Cos 66°: 0.4067366. . .
• Cos (-66 degrees): 0.4067366. . .
• Cos 66° in radians: cos (11π/30) or cos (1.1519173 . . .)

What is the Value of Cos 66 Degrees?

The value of cos 66 degrees in decimal is 0.406736643. . .. Cos 66 degrees can also be expressed using the equivalent of the given angle (66 degrees) in radians (1.15191 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 66 degrees = 66° × (π/180°) rad = 11π/30 or 1.1519 . . .
∴ cos 66° = cos(1.1519) = 0.4067366. . .

Explanation:

For cos 66 degrees, the angle 66° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 66° value = 0.4067366. . .
Since the cosine function is a periodic function, we can represent cos 66° as, cos 66 degrees = cos(66° + n × 360°), n ∈ Z.
⇒ cos 66° = cos 426° = cos 786°, and so on.
Note: Since, cosine is an even function, the value of cos(-66°) = cos(66°).

Methods to Find Value of Cos 66 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 66° is given as 0.40673. . .. We can find the value of cos 66 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 66° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 66 degrees as:

• ± √(1-sin²(66°))
• ± 1/√(1 + tan²(66°))
• ± cot 66°/√(1 + cot²(66°))
• ±√(cosec²(66°) - 1)/cosec 66°
• 1/sec 66°

Note: Since 66° lies in the 1st Quadrant, the final value of cos 66° will be positive.

We can use trigonometric identities to represent cos 66° as,

• -cos(180° - 66°) = -cos 114°
• -cos(180° + 66°) = -cos 246°
• sin(90° + 66°) = sin 156°
• sin(90° - 66°) = sin 24°

Cos 66 Degrees Using Unit Circle

To find the value of cos 66 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 66° angle with the positive x-axis.
• The cos of 66 degrees equals the x-coordinate(0.4067) of the point of intersection (0.4067, 0.9135) of unit circle and r.

Hence the value of cos 66° = x = 0.4067 (approx)

☛ Also Check:

• cos 360 degrees
• cos 10 degrees
• cos 135 degrees
• cos 19 degrees
• cos 570 degrees
• cos 450 degrees

FAQs on Cos 66 Degrees

What is Cos 66 Degrees?

Cos 66 degrees is the value of cosine trigonometric function for an angle equal to 66 degrees. The value of cos 66° is 0.4067 (approx)

What is the Value of Cos 66° in Terms of Sec 66°?

Since the secant function is the reciprocal of the cosine function, we can write cos 66° as 1/sec(66°). The value of sec 66° is equal to 2.458593.

How to Find the Value of Cos 66 Degrees?

The value of cos 66 degrees can be calculated by constructing an angle of 66° with the x-axis, and then finding the coordinates of the corresponding point (0.4067, 0.9135) on the unit circle. The value of cos 66° is equal to the x-coordinate (0.4067). ∴ cos 66° = 0.4067.

What is the Value of Cos 66 Degrees in Terms of Tan 66°?

We know, using trig identities, we can write cos 66° as 1/√(1 + tan²(66°)). Here, the value of tan 66° is equal to 2.246036.

How to Find Cos 66° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 66° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(66°))
• ± 1/√(1 + tan²(66°))
• ± cot 66°/√(1 + cot²(66°))
• ± √(cosec²(66°) - 1)/cosec 66°
• 1/sec 66°

☛ Also check: trigonometric table