Cos 67 Degrees

The value of cos 67 degrees is 0.3907311. . .. Cos 67 degrees in radians is written as cos (67° × π/180°), i.e., cos (1.169370. . .). In this article, we will discuss the methods to find the value of cos 67 degrees with examples.

• Cos 67°: 0.3907311. . .
• Cos (-67 degrees): 0.3907311. . .
• Cos 67° in radians: cos (1.1693705 . . .)

What is the Value of Cos 67 Degrees?

The value of cos 67 degrees in decimal is 0.390731128. . .. Cos 67 degrees can also be expressed using the equivalent of the given angle (67 degrees) in radians (1.16937 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 67 degrees = 67° × (π/180°) rad = 1.1693 . . .
∴ cos 67° = cos(1.1693) = 0.3907311. . .

Explanation:

For cos 67 degrees, the angle 67° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 67° value = 0.3907311. . .
Since the cosine function is a periodic function, we can represent cos 67° as, cos 67 degrees = cos(67° + n × 360°), n ∈ Z.
⇒ cos 67° = cos 427° = cos 787°, and so on.
Note: Since, cosine is an even function, the value of cos(-67°) = cos(67°).

Methods to Find Value of Cos 67 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 67° is given as 0.39073. . .. We can find the value of cos 67 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 67 Degrees Using Unit Circle

To find the value of cos 67 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 67° angle with the positive x-axis.
• The cos of 67 degrees equals the x-coordinate(0.3907) of the point of intersection (0.3907, 0.9205) of unit circle and r.

Hence the value of cos 67° = x = 0.3907 (approx)

Cos 67° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 67 degrees as:

• ± √(1-sin²(67°))
• ± 1/√(1 + tan²(67°))
• ± cot 67°/√(1 + cot²(67°))
• ±√(cosec²(67°) - 1)/cosec 67°
• 1/sec 67°

Note: Since 67° lies in the 1st Quadrant, the final value of cos 67° will be positive.

We can use trigonometric identities to represent cos 67° as,

• -cos(180° - 67°) = -cos 113°
• -cos(180° + 67°) = -cos 247°
• sin(90° + 67°) = sin 157°
• sin(90° - 67°) = sin 23°

☛ Also Check:

• cos 270 degrees
• cos 240 degrees
• cos 18 degrees
• cos 55 degrees
• cos 7 degrees
• cos 106 degrees

FAQs on Cos 67 Degrees

What is Cos 67 Degrees?

Cos 67 degrees is the value of cosine trigonometric function for an angle equal to 67 degrees. The value of cos 67° is 0.3907 (approx)

How to Find the Value of Cos 67 Degrees?

The value of cos 67 degrees can be calculated by constructing an angle of 67° with the x-axis, and then finding the coordinates of the corresponding point (0.3907, 0.9205) on the unit circle. The value of cos 67° is equal to the x-coordinate (0.3907). ∴ cos 67° = 0.3907.

How to Find Cos 67° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 67° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(67°))
• ± 1/√(1 + tan²(67°))
• ± cot 67°/√(1 + cot²(67°))
• ± √(cosec²(67°) - 1)/cosec 67°
• 1/sec 67°

☛ Also check: trigonometry table

What is the Value of Cos 67 Degrees in Terms of Sin 67°?

Using trigonometric identities, we can write cos 67° in terms of sin 67° as, cos(67°) = √(1 - sin²(67°)). Here, the value of sin 67° is equal to 0.9205.

What is the Value of Cos 67° in Terms of Cosec 67°?

Since the cosine function can be represented using the cosecant function, we can write cos 67° as [√(cosec²(67°) - 1)/cosec 67°]. The value of cosec 67° is equal to 1.08636.