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. . .
![Cos 67 Degrees](https://static.qumath.in/static/website/old-cdn-static/trigonometry/cos-67.png)
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
![value of cos 67](https://static.qumath.in/static/website/old-cdn-static/trigonometry/value-of-cos-67-degrees.png)
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:
Examples Using Cos 67 Degrees
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Example 1: Simplify: 7 (cos 67°/sin 157°)
Solution:
We know cos 67° = sin 157°
⇒ 7 cos 67°/sin 157° = 7 (cos 67°/cos 67°)
= 7(1) = 7 -
Example 2: Find the value of cos 67° if sec 67° is 2.5593.
Solution:
Since, cos 67° = 1/sec 67°
⇒ cos 67° = 1/2.5593 = 0.3907 -
Example 3: Find the value of (cos² 33.5° - sin² 33.5°). [Hint: Use cos 67° = 0.3907]
Solution:
Using the cos 2a formula,
(cos² 33.5° - sin² 33.5°) = cos(2 × 33.5°) = cos 67°
∵ cos 67° = 0.3907
⇒ (cos² 33.5° - sin² 33.5°) = 0.3907
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.
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